Current Army here!
My experience may be different from yours, as I'm (1) combat support and (2) (possibly(still questioning)) ftm.
HOWEVER, I do know that there are huge provisions being made- you are allowed to receive the medical treatment once it is "determined medically necessary." What I have taken this to mean is "once you see a provider about the dysphoria and tg feelings and they give you the go-ahead on beginning transition." Currently, I'm exploring options with my Army psychologist about my thoughts on this, and we're looking into the feelings together. The behavioral health I have received has been a surprisingly very positive experience- most *behavioral* providers are very open and willing to work with you to whatever goals you may have. (I emphasize behavioral because we all know how difficult the regular medical system can sometimes be.) So as far as the actual transition process, you have the option and it is available. You can't start HRT on deployment, and you can't start it within I think a few months after, but once you're on it, you are undeployable for (if I remember correctly) two years AFTER becoming stable. Bottom line is, its a treatment that's there, but you have to go through the right avenue- and yes, it does have to be at the convenience of the Army, but that's everything really.
Being infantry, I could see how that might affect you- referring back to the whole "convenience of the Army thing... But as long as you are not slated for a deployment in the near future, you technically *should* be okay, but I'm not really sure how alot of the infantry field training schedules work, that's something you'd have to discuss with your leadership when/ if you decide to follow this while still enlisted.
Another option, if it becomes apparent that transitioning as infantry would not be possible... a reclass. I guess here you have to weigh a couple of things. Is transitioning while still in what you want to do? Do you only want to be infantry/ CA? Is it a deal-breaker for your continued enlistment to have to consider a reclass to a CS MOS in order to transition? Is it a deal breaker for transitioning? Which one would you consider more important to you? etc. I know the atmosphere is tough. I have to remind my comrades almost once a week to refrain from using "gay" as a derogatory word (by saying "that's gay" meaning "that sucks" or "that's stupid") because I know they could get in serious trouble for it if the wrong person walks by (it also bothers me a little, tbh). But for the most part, everyone tries to be tolerant at least, if they're not exactly accepting, of lgbtq people. This doesn't go for everybody, but for the most part it rings true, at least in my experience. I know that it is a huge EO deal right now, and they actually CAN'T say anything negative to you about it, I don't know if you get an EO brief annually, though. I know there's alot of differences between CA and CS units... I wouldn't begin to know what the atmosphere is in CA, but usually a simple OTS correction does the trick for me. Someone says/ does something, I correct them, we go about our merry way. The biggest asset you have as far as your comrades and the environment you create as a group of people is your voice, and sprinkle some patience in there. A lot of soldiers have never been exposed to these things, so being patient with them and their unintentional ignorance (I'm not trying to use that negatively, I just don't have a better word) is going to be a big part of your life. Much of the time, comedy is a way to diffuse the tension and process an idea- we see it in our political satire comics. This is why everyone makes jokes at/ after those kinds of briefs. Joke about it with them at the level you see as being appropriate for your environment, laugh with them about it, and educate them gently on what is not okay when they take it too far. That's the best advice I think I have for this area...
Bottom line: Its something that you're going to have to assess and explore- there are options out there, but some of them may or may not be appealing. And that's okay. At the very least, please do go see a therapist about it when you get home. They're helpful, and can help you know more about what your options and rights in this department are.
If you have any questions/ comments/ concerns (I know, I think I'm hilarious), please feel free to shoot me a message and I'll do my best to answer anything you don't already know, and if I don't know the answer, I'll work on finding it since being deployed infantry and being deployed MI are two different environments, and I probably have a little bit more freedom in the research area than you right now. I am more than happy to help any way I can.