It's unprofessional in the extreme. If you have equal-employment protection or trans-friendly policies and you've corrected them enough that you're sure it's not an honest mistake, you need to go to your boss.
Here's the issue as I see it. Any business loses money on new hires. They don't want to spend two months getting you productive and then have to find a replacement because you've been bullied into quitting. The fact that this is coming from established employees may weaken your position - if they're more valuable than you are.
On the other hand, if they're motivated by jerkishness, they've probably been jerks before. In that case, the boss is either comfortable putting them back in line or is looking for a chance to fire them.
The best course of action depends on existing social factors. Sorry that you have to suss that out.
So, "professional." You and they both have an obligation to represent the business well in front of customers. Not even being able to consistently gender one of the employees makes the business look really foolish.
I wouldn't correct them in front of a customer. I would correct at the earliest possible opportunity.
And if it becomes awkward or tiresome, then go to the boss anyway. Always approach The Boss doing your best to solve a problem for him or her.
Like, if you're working retail for example, you're in the thick of HRT, and you're out to your boss.
- I'd like to talk about how my gender is perceived by customers. ... So here's the thing: my doc and therapist say I can expect further visible results from my hormone therapy in the future, but now most people can see me as male or female depending on how I'm introduced. Some of the other employees say to customers things like "she'll help you," when, I believe, "he'll help you" would appear just as professional. It certainly will over the next several months as my appearance and voice continues to change, but I'd like to settle this issue soon. Can you back me up if I talk to them?
And to the employees, correcting a mis-step.
- Hey, listen, if I'm handing a customer off to you, I'd say "she'll help you." Please get my gender right too.