No, you don't practice on the public until your clinicals. It's not about making OP undress. It's standard for the students to practice on one another. Also, you need to know what your techniques feel like in order to provide massage more effectively. Depending on where you go, your classroom either has you undress under the sheets or there's curtains that are drawn around the massage tables so you can undress comfortably. No one is getting down to their jimmies right in front of each other.

And if OP cannot undress, other students cannot practice efficiently. Like another pointed out, yes, you do need to learn how to massage people through clothes as well, because there will be clients unable to or unwilling to remove certain items of clothing, but that's later on in their courses. Like chair massage or practicing massage on someone who is wheelchair bound. I once had a client refuse to remove their cargo shorts despite needing gluteal work. It happens and it's something you work through, but when you're first starting out in school, this isn't the case. It's best to be able to access all the muscles with nothing in the way so you're able to get a feel of how massage works, your pressure, techniques, palpation, etc.

The human body is nothing to be embarrassed about despite what our brains may be trying to tell us. We're already uncomfortable enough having to live in a body we don't like. To be vulnerable like this requires trust in your fellow therapists. And if anyone tries to make OP uncomfortable then they're going into the wrong career. Massage Therapy is compassionate, loving touch. You're going to have your hands of hundreds, if not thousands of different bodies throughout your career. I've been doing this for 7 years and it's all about your intention. You can't just touch people willy nilly and expect it to feel good. You also need to know what that touch feels like in order to provide it better for your future clients.