It’s not like there are people checking for immortals, I think it would be flagged by a dmv employee or something when they dont believe a clear 21 year old is actually 150. Let’s assume it’s current day im caught and not bring speculation on what the US is like in the year 2139 is like.
It’s been awhile since I’ve seen it, but IIRC, the film isn’t saying the Christian Jesus we all know about is immortal, but that this character in the film who is immortal (and a white dude, BTW) was assumed to be the son of God because people 2,000 years ago found out he was immortal and had no other explanation.
ETA: Looks like I remembered reasonably well. Here’s the scene in question: https://www.youtube.com/watch?v=6bXtdr5BI74