Here we are treading into waters where I just don’t know enough about you, or you about me for that matter, to be totally clear where we are respectfully coming from. This is just a common problem with an on line forum.
It might be useful if you flatly clarified what you would consider to be the false Christ and the false gospel in play in this instance. For you appear to be wanting a much larger discussion than I initially offered.
I will go first with some easy to reach fruit: like Islam a false gospel may teach that the faith was lost or corrupted, requiring a new prophet to give a new message, one which not incidentally will teach entirely new things about salvation, about creation, or any number of things important enough to drag those who give heed off of the reservation, so to speak.
I do not know if this is what you might be referring to, and it does not really seem to line up with either extreme option that might be tied into your earlier comment about Protestants calling the RCC a thing of the Antichrist because simply I don’t know that either Protestants or the RCC were talking about the other as if the other were claiming to be new prophets.
Pm to you