I do agree that it's worth keeping the fakes, though. If the Museum of The Bible were bigger on "museum" than "bible" this would be a great centerpiece for an exhibit on the long history of profitable religious forgeries.
[1] https://www.sciencemag.org/news/2019/02/researchers-hung-men...
[1] https://m.ncregister.com/blog/smcafee/i-made-a-third-class-r...
Clearly it is not something worthy of a museum then. A fake thing being old doesn't make it historically significant for a museum. A church, maybe.
No relics? less travel? Slower "flatten the curve" back plague? Smaller renaissance? Weaker atheism today? :O
Unfortunately I tend to focus on the atrocities that have happened in history in the name of the religion itself. Perhaps that would make a good topic to build a museum about.
Now, if more broadly you are referring to relics in the generic sense of objects of historical importance surviving from times long ago, then it seems obvious that most Christian relics are NOT fakes. Christianity has a long, deep history that has influenced the creation of massive amounts of art, literature, architecture, pottery, etc.