Do Protestants believe it is easier for New Testament believers to fulfill the moral law than it was before Christ?

A key passage which might seem at first blush to indicate New Testament believers have an easier time fulfilling God's moral law than Old Testament believers is Romans Chapter 8, an excerpt of which I include here:

8 There is therefore now no condemnation for those who are in Christ Jesus. 2 For the law of the Spirit of life in Christ Jesus has set me free from the law of sin and death. 3 For God has done what the law, weakened by the flesh, could not do: sending his own Son in the likeness of sinful flesh and for sin,[a] he condemned sin in the flesh, 4 in order that the just requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit. 5 For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit set their minds on the things of the Spirit. 6 To set the mind on the flesh is death, but to set the mind on the Spirit is life and peace. 7 For the mind that is set on the flesh is hostile to God; it does not submit to God’s law, indeed it cannot; 8 and those who are in the flesh cannot please God. 9 But you are not in the flesh, you are in the Spirit, if in fact the Spirit of God dwells in you [my emphasis].

While the Holy Spirit of God was obviously at work in the Old Covenant, his presence vis a vis true believers was sporadic--spasmodic, even! Under the New Covenant, true believers receive the indwelling presence of the Holy Spirit. And while both Old- and New Covenant believers could choose to live their lives apart from the will of God, the Holy Spirit is never spoken of in the New Covenant as departing from a believer, but he is in the Old (see 1 Samuel 16:14; cf. 1 Samuel 10:6).

Instead, a regenerated believer can walk by, be filled by, be led by, and live according to the Holy Spirit. By the same token, however, that believer can also grieve the Holy Spirit (Ephesians 4:30), quench the Holy Spirit (1 Thessalonians 5:19), and lie to the Holy Spirit (Acts 5:3).

I'm sure the Holy Spirit was grieved by recalcitrant believers under the Old Covenant (see Isaiah 63:10), but the same Spirit was not an indwelling presence in the same way he is under the New Covenant.

What, then, might we legitimately conclude about the ease or difficulty of fulfilling God's moral law, BC and AC (i.e., before Christ and after Christ)? Frankly, I do not think there is an easy answer to your question. To say, "The Holy Spirit does it all for us today" is partially true, but we Christians have the responsibility to "walk by the Spirit," or "to keep in step with the Spirit," and to obey the Holy Spirit. With privilege comes responsibility, and responsibility means conscious obedience to the Spirit's promptings.

Yes, we Christians are to "work out our own salvation," but by the same token "God is at work in us both to will and to do according to his good pleasure" (Philippians 2:12-13). We as Christians know that by the works of the Law no one is justified. Justification is God's doing; obedience is ours. When we disobey, the Holy Spirit does not abandon us; he abides. Old Testament saints were never cast aside by God for disobeying any or all of the 613 commandments in the Tanakh, but I think we are safe in saying that both Old- and New Testament believers alike find total and complete obedience to God's moral law an impossibility.

The rich young ruler who told Jesus, "All these things I have kept from my youth” went away sad because he was very wealthy (see Luke 18:18-27). Both Old- and New Testament saints realize that complete and total obedience to God is an impossibility. And while God does not grade us on the curve, he did and does impute his righteousness to us freely as a gift of grace, regardless of where in salvation history we happen to find ourselves. Now that is easy. Everything else is a struggle, regardless of where in salvation history we happen to find ourselves.

Welcome to the group. I'm new here myself.

Do those verses show that the Christian is more able to fulfill God's commands than the old testament believer was? No, they do not, but maybe not in the way you might initially think.

Jer 31:33 and Ezek 36:26 are both in the OT, and indicate that they are the only way to fulfill God's commands. Your question assumes that the moral law could be fulfilled in the OT in a different way than in the NT. That's not the case at all.

Paul goes into some detail on this point.

knowing that a man is not justified by the works of the law but by faith in Jesus Christ, even we have believed in Christ Jesus, that we might be justified by faith in Christ and not by the works of the law; for by the works of the law no flesh shall be justified. Galatians 2:16

Note here that no flesh shall be justified by the works of the law. There is no distinction between OT and NT, Jew or Gentile. In short, it is impossible to be justified by anything other than faith in Christ.

For as many as are of the works of the law are under the curse; for it is written, “Cursed is everyone who does not continue in all things which are written in the book of the law, to do them.” Galatians 3:10

If one chooses the path of the works of the law, the only way to avoid a curse is to keep them all, all the time. But faith in Christ is the only viable option because nobody, OT or NT, Jew or Gentile, has kept the law perfectly. Paul spends a big chunk of Romans explaining this.

For as many as have sinned without law will also perish without law, and as many as have sinned in the law will be judged by the law Romans 2:12

for all have sinned and fall short of the glory of God, Romans 3:23

Whether without the law or in the law, we are judged and destined to perish because all of us have sinned and fall short.

What then shall we say that Abraham our father has found according to the flesh? For if Abraham was justified by works, he has something to boast about, but not before God. For what does the Scripture say? “Abraham believed God, and it was accounted to him for righteousness.” Romans 4:1-3

For the promise that he would be the heir of the world was not to Abraham or to his seed through the law, but through the righteousness of faith. Romans 4:13

Here Paul points out that the promise was given to Abraham through faith, not the law. Right at the source of the chosen people, the path to righteousness has been faith.

Therefore, if an uncircumcised man keeps the righteous requirements of the law, will not his uncircumcision be counted as circumcision? And will not the physically uncircumcised, if he fulfills the law, judge you who, even with your written code and circumcision, are a transgressor of the law? For he is not a Jew who is one outwardly, nor is circumcision that which is outward in the flesh; but he is a Jew who is one inwardly; and circumcision is that of the heart, in the Spirit, not in the letter; whose praise is not from men but from God. Romans 2:26-29

So here we find Paul's encapsulation of what true conversion is, for both Jew and Gentile. To be truly one of God's chosen people, a true Jew so to speak, one must be a Jew inwardly. Circumcision of the flesh has no moral worth in itself because circumcision of the heart is and has always been what truly counts. So also, outward compliance with the law, in whatever imperfect form it may take (see Isaiah 64:6), has no moral worth in itself because inward compliance with the law is and has always been what truly counts.

A believer in the OT could fulfill God's law in exactly the same way as a Christian does, by participating in the New Covenant promise of that law being written in the heart and mind. So the answer to your question is, No.

Now you might wonder how someone during OT times could be part of the New Covenant. But that's for another time.