In my view, Paul suffered because he was an Apostle, but I think its within reason to say some of his suffering was because he was Christian, yes. Rome showed no prejudice in their lust to punish the believers in God, no matter what you would label those believers. The followers of " The Way" suffered before they switched their name to Christian, and suffered after.
Does the term " Christianity' deserved to be lifted up like the term " Christ?" Well because they are so closely related, the term Christian has become just as holy as Christ; to the Christians that is. That is one of the reasons " Christmas" is so revered, because it contains within it" Christ."
One could separate Paul's suffering from Christianity, or include it with it; and either way, in my view, be correct.
Join the great host of wall tappers, folks that haves to tap their way along the wall even in bright sunshine...they are blind. They all think they are better informed than the rest of us lowly plebs. They have a handle on things...they are at the crux of the matter.
Wise in their own conceits
Let someone come along and say to them "I have found Him of whom the prophets speak....He is altogether lovely and fair, He hath dealt kindly with my soul"
They may afford a pleasant comment upon that, "that's nice" they say.
But it totally DISproves your theory, it PROVES that the church is everything it ever was, everything that God wants it to be. It STILL has the ancient power to impart the truth that brings PEACE to the human soul, JOY to the inner man, LOVE to the human heart. It still is able to share the keys that will solve people's hardest trials, the church still has the power to heal.
As long as the message is being preached "JESUS SAVES" as long as people hear it and believe it and can call upon Him.