My 16 year old son is drinking gainer protein shakes after lifting. Bilirubin level 3.8. Could this be related?

The trouble with. Taking dietary supplements they're not regulated, many come from China and you're not sure what's really in them. I would stop taking and get checked out.
Hard to say. It's possible but most pure protein shakes are fairly safe. Did he have a normal bilirubin before he started the shakes? any symptoms? any other lab abnormalities? all questions that should be discussed with his doctor. Probably a good idea to stop the protein shakes and recheck the bilirubin.
Could be. Yes it could be related. I could also be that his is taking something else, that you are not aware of, which could be a greater prob. Another possibility is that there is another medical/liver issue going on. Stop any potential problematic agents and recheck the blood test in a month. If still high, he'll need further studies: blood tests & at least an ultrasound of his liver and gall bladder.