How is it possible to have a high view of the authority of the Bible and a positive view of textual criticism?

Because we wouldn't know what the Bible says without textual criticism. Textual criticism is just concluding what the original text (the autographs) said, so I would say that anyone who has attempted to accept or conclude what is the "original text" has engaged in textual criticism, including those that compiled the text in the first few centuries.

"Textual criticism" is the critical examination and comparison of the manuscripts of the biblical text to determine the proper readings of the biblical text. This is how the accurate transmission of Scripture can be confirmed. Hence, a "critical" edition of the Greek New Testament, such as the NA28 (read it online) or UBS 5 (read it online), usually means that all the variants in the manuscripts are noted and the alternatives (if any) are noted in which manuscripts in the "apparatus." This, in English Bibles, comes in a much much less detailed fashion as footnotes. Notes such as "the earliest manuscripts don't have x" or "Some manuscripts say xyz." The most prominent and biggest examples of this that is obvious in most English translations would be the notes saying the earliest manuscripts and many other ancient "witnesses" don't include Mark 16:9-20 and John 7:53-8:11.

I would say the only reason we can have a high view of the authority of Scripture is because of textual criticism. Specifically, if textual criticism (e.g. comparing all the early Greek manuscripts) determined that all the Greek manuscripts differed horribly (as do some other important historical and religious texts...) then there would be good reason to doubt their accurate transmission. However, the similarity upwards of 99% serves to reinforce the validity of the transmission of the text.

Furthermore, the Chicago Statement on Biblical Inerrancy states in Article X

We affirm that inspiration, strictly speaking, applies only to the autographic text of Scripture, which in the providence of God can be ascertained from available manuscripts with great accuracy. We further affirm that copies and translations of Scripture are the Word of God to the extent that they faithfully represent the original.

We deny that any essential element of the Christian faith is affected by the absence of the autographs. We further deny that this absence renders the assertion of Biblical inerrancy invalid or irrelevant.

The highest view of Scripture, inerrancy, (according to evangelicals at least per this statement) applies only to the autographs, which are the manuscripts that the apostles wrote down "as they were carried along by the Holy Spirit." The Bible does not say that God carried along the scribes or copyists by the Holy Spirit, and thus we should not be thrown off-guard by the fact that there are errors in the manuscripts that we possess due to copyists or others. The textbook mentioned below has a chapter on types of errors in the manuscripts. Important note: the textbook and that chapter specifically gives examples of errors not only in manuscripts but also by the author (this was a section probably written by Ehrman, though I haven't looked at the 3rd or prior edition to compare), which many would deny. I have examined a couple of his proposed errors and determined they were unfounded claims.

The important thing is that the autographs "can be ascertained from available manuscripts with great accuracy." I also want to make clear here that we do not have the autographs, the actual writings that the apostles wrote, but only copies that were subsequently made. While this is a bummer (in my mind), this does not noticeably lesson our confidence in Scripture or even in our English translations (given their basis on the most up-to-date authoritative manuscripts). The autographs may also be found. However, currently, the oldest "extant" manuscript we have is the John Rylands Papyrus 52, which dates to early 2nd century. I think those who have studied textual criticism, especially in comparison with other ancient documents or even the Quran or other later texts, may come to agree with the conclusion that it indeed is "by the providence of God" that we have so reliable of a transmission of the text. It is absolutely astounding.

Our 5800+ stack of Greek manuscripts plus the hundreds of translations within a few centuries that align 99+% serve to demonstrate the importance and reliability of the Scripture, especially when you look at the 5-10 copies of manuscripts from the Greek philosophers, and 6 of the early Quranic manuscripts, some of which are missing 25% chunks out of it and all are different than today.

It is through textual criticism and new discoveries (e.g. Dead Sea Scrolls!) of manuscripts that we know how the KJV is lacking because of its basis on the textus receptus (text compiled by Erasmus in the 16th century). It is how we know some cases of more reliable readings from the Septuagint (LXX) rather than the Masoretic text, and vice versa (I just discovered the world of LXX textual criticism the other day, where I found Rahlfs' semi-critical LXX and the 70+ year project of the full-critical Gottigen LXX and Cambridge LXX).

Summary: Textual criticism is an extremeley useful field (critical even) to support the reliability and authority of the transmission of the text and the Bible as a whole.

Resources:

The Text of the New Testament: Its Transmission, Corrruption, and Restoration by Bruce Metzger and Bart Ehrman

Note: Metzger is neo-orthodox and Ehrman is agnostic.

Note 2: I have answered focusing primarily on New Testament textual criticism. That has been more of my study and seemingly the "go-to" focus of text-critical questions. This is interesting because I bet textual criticism for the Masoretic text, which wasn't truly final until the 9th-11th century AD though agrees with proto-Masoretic texts and the LXX greatly, would probably be even more difficult, spanning many more centuries (~35 centuries comparied to 20 centuries, which is more than 50% longer time period, and yet we have only a more recent extant Hebrew Bible compared to New Testament). However, the more trained and disciplined scribes helped to limit the textual variants in comparison to the NT. There is evidence of variations that are due to scribal school differences.

A Note on the Percent of Accuracy of the New Testament Text: Norman Giesler quotes several experts in concluding that the NT is "98.33% pure," "99.75% accurate," and "99.9% free of real concern."

To be honest, I'm not sure what leads you to ask the question. Almost all Christians and almost all Christian denominations/movements have a positive view of textual criticism.

The facts are that humans are fallible document copiers, and we therefore have thousands of manuscripts with minor differences. And as much as classicists and historians value the process of textual criticism, we Christians who believe the Bible is the inspired word of God have even more reason to want the original texts he inspired and therefore welcome textual criticism as a tool.

Textual criticism isn't foolproof, and its results are always a work in progress. Neither can it determine our doctrine of inspiration. An example I often give is the book of Jeremiah, whose Greek text is one eighth shorter and arranged in a different order to the Hebrew Masoretic Text. The Dead Sea Scrolls have manuscripts corresponding to both versions, and both versions have been accepted as scripture by Christian groups in history. Our doctrine of inspiration has to be robust enough to handle this. Some Christians only accept the Hebrew text. But as many scholars think the Hebrew is an expansion of the Greek (or the Hebrew it was translated from), so should we rip out the longer version from our Bibles and replace it with the shorter? I think our doctrine of inspiration should actually uphold these two text families, so that we don't conclude that the Greek text the Apostles read an quoted was actually a completely uninspired error. Whatever you think, textual criticism can't determine which of these text families is inspired, but it can help us determine what the Hebrew and the Greek texts should each look like.

Tricky cases like Jeremiah aren't really that common. Most of the time textual criticism has a fairly simple question to answer. Paul (and his scribe Tertius) wrote the letter of Romans. It was copied thousands of times, and many small errors crept in. The question for textual criticism is simple: what is the original text of Romans? It's not easy to answer, and takes lots of work, and different scholars have varying philosophies and methods, but the question itself is a simple one. Christians who recognise the high authority of the Bible welcome textual criticism as it tries to answer this question.

Perhaps another way to answer the OP is to say that it is based on a false contrast. As an analogy, consider the following sentences:

1. Jazz is the best kind of music and country is the best kind of music.
2. Jazz is the best kind of music and the trumpet is the best instrument.

In the first sentence there is a contradiction because the contradictory opinions relate to the same category. But in the second sentence there is no contradiction because the categories are not the same. A musical style is not identical to a musical instrument.

In the same way, textual criticism and authority are not the same category. Textual criticism answers the question, "What is the correct content of the original document?" Authority answers the question, "Is this document one which I should accept as true and normative?" Two different questions.

A simple illustration may assist. The apocrypha are a set of inter-testamental writings that are accepted as authoritative by some but not all sections of the Christian church. A Catholic may accept 1 Maccabees as part of his authoritative bible; a Baptist may not. But both of them, if they choose to read 1 Maccabees, would want to read the most accurate version of that text that is available. The debate over the authority of 1 Maccabees is based on different grounds than the mere determination of the text.