Your ID is - according to the law - supposed to look like you do. Duh-O. They are supposed to be able to ID you from it. If it does not look like you then the authorities (be it cops or the guy at the liquor store) don't have to accept it. And if the cops don't accept it, well you'll have a couple hours of suck while they figure it out.
The reason the law in MA is coming on-line is because so many places in MA already tolerate and accept it. So I doubt that there is going to be some sort of wave of firing TG people between now and June. Still you can use the law as a target, start getting all your duck in a row now. It takes somewhere between a few days and a few months (depending) to get the First Step done, so you could start the process, then when the law kicks in you'll be able to come out and be out.
When you do this, it's best to do it as a real cleaning out of the Aegean Stables deal - ie. do a marathon to change all your ID everyplace as part of one huge task. There is an order that you have to go in, and I'm sure people who've done it could make a road map for you. But first court for a judge's decree, then DMV, then bank, then your library card, and so on.