In certain productions such as, oh, Les Miz.
Copious amounts of Zoloft is all I can think of.
I’ve seen Bernadette Peters bawling like a baby through songs, so I don’t know that they keep from getting emotional necessarily.
It’s their job. They are faking emotions to fool you into investing emotion.
Repetition.
I never did musical theater, but I did a fair bit of acting once upon a time. After the 2nd week or so of rehearsals, you have to start working again to find the emotion that hit you the first time you read through the script, because it’s all just become words at that point. I imagine songs work somewhat the same way.
This is one reason I don’t watch my favorite movie of all time as often as ones I like less. I don’t want repetition to dull it for me.
Part of practice is finding the honest emotion, and part of practice is keeping the emotion under control. An actor who can’t keep it together is not a good actor, nor is one who can’t portray/experience real emotions.
And that’s why I quit. 
Re: Acting…for the same reason, I won’t usually watch scenes I’m not in, nor will I drill lines so much that it isn’t fresh anymore.
HOWEVER: There are plenty of professional actors and playwrights who will say, “Just say the fucking lines. Stop trying so hard to ‘keep it fresh’. You’re an actor, act. Don’t try and feel every line like you’ve never said it before.”
To each their own.
And that’s why I music direct; I just tell them what I want, and they’re the ones who have to know how to do it well.
My local theatre will have Les Miz auditions soon. I was watching “Empty Chairs…” This afternoon…yeah, I won’t be using that. I don’t think they’re looking for someone whose voice keeps breaking and choking up.
I’ll probably do something funny or light as I’m not really shooting any higher than the Thernadiers (yes! I would totally play the mrs or the mr) or the chorus.
Some years ago, I read an article by someone who went to see Janet Jackson in concert. She did a slow, sad song onstage and struck a pensive pose, looking almost overcome with emotion. The writer went on to say he followed Ms. Jackson to another city and another concert, and observed she struck the very same pose during the slow sad song. Made the same gestures, same quiver in her voice at one point in the song, everything the same. It was all an act! Imagine that!
This thread is like the microcosm of the ‘it’s called acting’ school, vs the ‘method acting’ school.
Makes me wonder how many actors use both methods in different circumstances to get the best impact for any given scene/situation.
I’m a big fan of “Spring Awakening”, so I saw the first national tour several times in different cities. One song, “The Dark I Know Well”, about child abuse, evoked tears from the performer, Sarah Annette Hunt, at every performance. It may have been acting, but this show allowed audience members to sit onstage, so I was sitting right next to her at some performances and she seemed genuinely affected each time to me.