So - there's no reason to believe this is true. Part of how we can gage truthfulness of Biblical passages on whether or not they are attested to elsewhere, and this factoid - this story about Mary and Elizabeth is not found anywhere else. We know very little about John the Baptist, and we have no source other than Luke that even names John's mother as a woman named Elizabeth. The Gospel of Luke was probably written in 80-90 CE, probably 60 years after John's execution (an execution we believed happen because other, non-Christians wrote about it too). As discussed in this article, Luke would have adequate reason to make this up - and probably no way of knowing if it were true.

We can further doubt this passage's truthfulness because it comes in a story that contains other details we know to be false: there was no census in the time frame that Luke states, nor would a census require any travel, and Luke gets the details of the purification ritual incorrect. You can read more about the problems with the infancy narratives here: https://medium.com/@andrewspringer/what-youve-heard-about-the-birth-of-jesus-isn-t-true-but-that-s-ok-bb6455721034

I would add that even if Jesus and John aren't related, it doesn't fundamentally change anything to your faith.