<<Nice story, but not the point of my question. Would listing religious preferences on a dog tag be considered proselytizing?>>
No, your question was if anyone had a problem with the dog-tag showing the soldier's religion.
I don't, if the soldier consents. I think he has a right to be free of any religious tags if that's what he wants. It's basically up to him.
As I understand it, I believe the religion is shown on the dog-tags in case the guy is mortally wounded and not able to communicate his religion to those around him - - he wants to be sure that he's given the proper last rites by those who really can get him through the Pearly Gates, and not by those other guys who can't. Well, if the guy's prepared to sacrifice his life for his country, the least his country can do in return is ensure that, if he believes in the afterlife, he'll get his best shot at a good one from someone who he believes has the best credentials to deliver the goods.
And, no, I don't think religious dogtags are proselytizing. I don't know of anyone converted to any religion from reading the dogtags hanging from anyone else's neck. If I wanted to proselytize, I'd find some better way to get the message out.