From the time of Muhammad onwards Islam has all in all been a successful, victorious movement for many centuries.

Psychologically speaking, it does not take much persuasion to join the party of the victors, and to this day, many people gather around the successful, whether they bring truth or not. For many people "success" is the proof that it works and hence is "true".

What does this observation have to do with the authenticity of the gospels?

It does not require much courage or conviction to belong to the victorious religion of Islam, which even allowes its followers to deny their faith / God / Muhammad without earthly or eternal consequences if their life is endangered because of it.

In contrast, Christianity was persecuted for the first 300 years of its existance and many were martyred for their faith, mainly because they refused to render even the slightest act of worship to the emperor or Rome, since worship belongs only to God.

Furthermore, denial of faith is not an option for a Christian and is considered treason to God. Therefore, the early Christians have naturally been people with a vital interested to verify the truth and trustworthiness in what they believe.

Though this pressure was not in the same way on the early Muslims, that doesn't mean they were not interested in making sure their faith was true and based on authentic records.
But it is for sure psychologically very unreasonable to assume the Christians were not interested in the authenticity of the scriptures which were the basis of their faith. Nobody dies easily for things he isn't very sure about.

This argument is only to support the authenticity of the New Testament and that the Christians were sure enough about that to put their life on the line for it. Whether they were not only historically authentic, but also truly from God, that is another question, and more is said about this in other parts of this web page.