What is the basis for saying that the Gospel of Thomas was accepted as scripture by early Christians?

The Gospel of Thomas contains sayings attributed to Jesus and is therefore a Christian 'gospel'. This means there were early Christians - whether of the first or the second century - who regarded it as scripture in at least the broadest sense. It can scarcely be said that people wrote down sayings they attributed to Jesus, copied, distributed and then carefully preserved copies of the document, yet did not regard it as sacred enough to be 'scripture'. As a result, I will take it as a given that there were some early Christians who regarded the Gospel of Thomas as scripture, even if this was not a belief held by all Christians of the time. The issue then becomes whether it is probable that GThomas was written during the first century.

Among conservative scholars, and perhaps most theologians, the key reason for believing that GThomas could not have been written as early as the first century is that it pushes back the origins of Gnostic Christianity into the first century. Particularly if GThomas can be dated to the middle of the first century, this also highlights the puzzling situation of such substantial theological differences existing within a single generation after the death of Jesus. To a large extent, these things can be resolved if we hold the line and date GThomas to the second century.

Among liberal scholars, a key reason for believing that GThomas was probably written as early as middle of the first century is that it has close affinities to the 'Q' document which, in order to be a useful hypothesis, must be dated to no later than Mark's Gospel (thus no later than the 70s). Many critical scholars do, however, recognise that the extant version of GThomas is probably not original, having been redacted with some material from the canonical gospels.

Lisa Haygood (The Battle To Authenticate 'The Gospel of Thomas') states in her abstract:

Many early Christian sects were aware of and accepted The Gospel of Thomas as authentic Christian scripture, despite its unorthodox, radical doctrine, igniting an ideological battle in and around the Thomasine communities of the ancient world. This ideological war is still raging and conflict renewed and amplified with the discoveries of the Greek and Coptic texts of The Gospel of Thomas in the first half of the 20th Century. Since its discovery, The Gospel of Thomas has presented scholars with ferocious debate, as serious probability exists that Thomas preserves an older tradition of the historical Jesus than that of the Synoptic Gospels. [my emphasis]

Haygood (ibid, page 4) cites Helmut Koester, who asserts that that GThomas at times reflects the most primitive stages of the Jesus tradition, concluding that “much of the material of The Gospel of Thomas . . . was probably written within ten to twenty years of Jesus’ death.”

Haygood goes on, to discuss a theory, put forth by Quispel, that the “Judaic Christian sayings were written down in 50 CE in Jerusalem” and edited around 140 CE. She says "scholars other than Quispel also estimate the original text may have been composed as early as the first century and probably in Syria."

Haygood does consider research that may point to a later date for the Gospel. On pages 5-6, she cites the research of John P. Meier, who believes the Thomasine collection reflect second century Gnosticism. Meier contends, “it is only in light of this strange mixture of mysticism, asceticism, pantheism and polytheism that many of the sayings of the Living Jesus can be understood.” She says that he further alleges that the Gospel of Thomas is wholly dependent upon the Synoptic Gospels. Some scholars have noticed thematic similarities to Luke, which they say can be evidence of dependence, although it can also be evidence of subsequent redaction of GThomas or even evidence that the author of Luke knew the Gospel of Thomas.

In her conclusion, Haygood says:

page 10: Reconstruction of The Gospel of Thomas suggests an origin within a very old collection of Jesus sayings that likely emerged from the Jerusalem Church. This gospel was then carried to Syria, perhaps as the result of missionary activity by the Jerusalem Church.
page 12: Since it’s discovery, The Gospel of Thomas has presented scholars with ferocious debate as the serious probability exists that Thomas preserves an older tradition of the historical Jesus and potentially, [citing Pakis, Valentine. "(Un) Desirable Origins: The Heliand and the Gospel of Thomas." Exemplaria 17, no. 2 (2005): 215-53.] “brings us closer to Jesus’ original words.”

This can only be a very short summary of the evidence for an early date for the Gospel of Thomas, and I am fortunate to be able to cite Lisa Haygood's excellent and concise summary of some of the arguments. I had to stop somewhere and I believe this answer provides sufficient information to show that there is a reasonable and rational conclusion that GThomas was written some time in the first century - probably no later than the 70s - and regarded by an early cohort of Christians as authentic scripture.