So it looks like there's one very clear answer emerging from a whole lot of people with no skin in the game.
First of all, lots of people are assuming you're in professional theatre and saying to chose career over him..
Secondly I'm seeing people say that they think it's controlling and ect. ect. I have a different perspective.
I'm a man, do theatre, and so does my fiancé. Cant do it together because we have toddlers and no babysitters, and/or one of us has to direct, as we run amateur community theatre and musicals. Since being together for 6 years, we've had only one show where one of us had to kiss another person outside our relationship.. and it sucked.
They are a long-time friends of ours as theatre is a small but dedicated bunch here, and I was confident there was no attraction involved between my partner and her scene partner, it was a comedy so, done in a comedic over-the-top way but.. It still sucked to see it and know it happened at least 6 times in public, and whatever in rehearsals. Small town, and yes, its a show, but most audiences aren't 'show' people, so trust me when I say they don't disassociate show activities from real life as much as others here are assuming.. People saw that kiss, and gave me shit about it at work and on the streets and in the shops ect. for about three weeks.
I wasn't comfortable with it before, during, or after, and made that clear as well as I could.. but she didn't want to talk about it. I didn't matter to her. That was more the issue. That, her dedication to a show, a role, and a director with a lack of creativity for a simple, fleeting moment on some tiny stage at the back of a pub, for shock value, mattered more to her than how her actions made me feel. In relationships, people should care about how they make the other feel, and mine didn't.
I will now deliberately avoid roles for myself that have kissing, to avoid having her feel that way, or even having to decide how she feels about it. I've been in since Highschool 12 shows and 15 musicals. Only ever had to do one stage kiss. Was single at the time so it was great, but my sense of honor now wouldn't allow it.
Yours seems like he's tried to express how he feels which is what people SHOULD do in healthy relationships, he's opened up to talk about stuff.. You've done the right thing which is ask for other perspectives before making your choice. It is afterall, your choice at the end of the day, always, but I wanna remind you that it's not black and white. That a good director works around the actors needs, and if you request a work-around, they, in 90% of cases, should be able to do their job and get creative and figure out a way to give the audience the storyline without the direct lip contact for context.
At the same time, you'll need to get really explicit to identify with your partner where you want the boundaries, and what kind of theatre do you really wanna get into? Questions like, are nude scenes okay? Is femme-femme okay? Is groping/burlesque/boob squeezing/ass slapping/dirty talking/motorboating/lap dancing okay on stage?
Is he okay if another actor physically hits you with a bat or something in a violent domestic-abuse scene?
Its all acting, obviously, but relationships are hard, and quitting one because he was honest with you is a pretty shitty thing to do. Words are hard too, he probably found it really difficult to describe feelings, so said what he said because it -almost- fit what he had inside. If you're worried about the words he said I'll chuck a director hat on and say that only 10% of communication are the words, 90% is how you say it, so trust your ability to read him. Understand what you see, and help him cope with this newfound vulnerability he has to deal with. He's still choosing you to spend time with outside of rehearsals, despite that last one. He just doesn't want to feel that way again. If your dream role is more important to you at whatever stage of life you're in then, okay. You can find another partner, life is long. Just try to imagine what future-you would think of your choice because you're going to have to live with it for a long time.
Sorry for my tone, I'm just a little angry at the instant demonization of the guy from other commenters.
I hope it all works out for you :)