If every state had their own tags and their own rules then it would be pretty easy to find the state with the weakest system and abuse the hell out of it. Just like with so many other state-by-state regulations. The best solution I can think of is a national tag system that is only given to recipients of professionally trained service animals and is hard to duplicate but easy to authenticate.
Could this be alleviated (not just on trains) if the states required a tag similar to the usual dog registration tag that says, "Service Animal"? It wouldn't have to list a medical condition if privacy is an issue; it could simply be a little yellow or red square or circle that is stamped, "Service Animal" and then some kind of registration number (like the regular dog registration). It would be easy to spot if the dog isn't already wearing one of those "Service Animal" vests, and it wouldn't reveal a medical condition. It would simply be an easy way to avoid questions.
Yeah Maine will probably start selling them to supplement their trailer license plate industry. It still something that should be looked at. It is not just for this reason but also so people know not to go up and just start petting the dog. The dog is working and relally shouldn't be disturbed.
At a minimum Amtrak (or any place that doesn't allow animals but are required to allow service animals) should be allowed to ask the person for proof that the animal is a service animal. This may be a letter (maybe notorized) by a physician and another document showing the animal is a trained service animal should suffice. While I am sure anyone could reporduce documents in today's world, at least it would keep the semi-honest or lazy on track.