I'm also a SLP who stutters. I almost failed a graduate placement because a supervisor (school setting) wasn't comfortable with me stuttering in front of children. She was wrong. Sadly, there's a lot of misunderstanding about stuttering even among the people who are supposed to be trained to understand it best. I can't say you won't face discrimination, but I can say that most SLPs are completely fine with me stuttering in front of people. The goal for 98% of our therapy isn't fluency anyway. And, stuttering isn't a behavior that you can train away.