Well i can also think of the dynamics of the relationship.... it could be that he somehow believes that if the two of you become "naked locker room buddies" that it will somehow diminish his effectiveness in being your coach.
I don't think that it's the gay/straight thing as much as him trying to place a boundary in place between your interactions when 'he is on the clock' and much like a doctor-patient relationship, you are subordinate to his physical interactions. You didn't mention whether or not the guy he was standing naked with was also a client- or just another club member...
Sometimes I think there's a natural level of trust and 'investment' that comes with allowing your body to be "displayed" to another guy in the locker room. It goes like this: you are in a strange place or visiting in another city, and you have the "F*ck it I'll never see these people again" attitude and so you either let it all hang out (full tilt exhibitionist behavior) or you are looking for 'good locker room nudity' at every opportunity, or you are on the opposite side- feeling shy and nervous about being seen by a group of strangers.
Once you're no longer the 'new guy' you get to the stage where you will probably see the same group of guys fairly frequently, since you are all working out on a similar regular schedule. Keep a friendly demeanor, and sometimes chat up a dude on the gym floor to eliminate the "creepy" factor, then you will have a few guys that you can comfortably have small talk with in the locker room. Look for opportunities to ask for a spotter on the weight bench, or ask someone how to do a specific exercise that he seems to be good at, etc. Remember your manners (say thank you if a buddy holds the door, etc) Make eye contact and smile when you see someone you recognize from a previous visit- say "hi how are you?" and see where it leads you.
After you are established a bit you will kind of know some of the regulars, and you might feel a bit more comfortable about in your own skin and not be preoccupied about what 'vibe' you are sending to others. And after being there and making small talk with strangers and hanging out a bit, you might find yourself the one standing naked in the locker room chatting up other members, or noticing that the guy sitting across from you is staring at your lap and allowing his uncovered body to be appreciated by you in return.
As for the trainer, he sounds like a douche bag. So you have to decide in a situation like this if you are happy with his paid services, or pick someone else to work with. You could call him out on his obvious social "walls" and directly ask him if he intentionally attempts to hide his social nudity from his clients as a policy, and if he denies it you can say "well I have noticed that it's just me" and I am feeling marginalized as a result- but since the theoretical solution would be "hey pal no offense intended let's go sit naked in the steam room together" isn't gonna happen- it's not worth it. Sad thing is that he's already defined his comfort level around you, accurate or not.
But there are other guys to chill with, if that's your thing.