Master’s program rejection with no reason. How to appeal?
Yes, that's totally normal. For example, my department typically gets 150-200 applications for the PhD program every spring, but we only accept ~20 students. That is a process that is exceedingly time consuming already as is. It is simply not reasonable to write up an explanation why the other 130-180 students were not accepted.

That's no different than for most job applications: The company you sent your application to will simply say "Sorry, we didn't choose you because we found someone who is better qualified", rather than giving you feedback where exactly they found your application lacking.

As for appeal -- I don't think any university has a process for this, but pretend for a moment that there were: What do you think would happen? The university made a determination that you were not as well qualified as someone else. You can appeal a decision if you think that a process was not followed, e.g., if your application had arrived in time but was rejected because the department (erroneously) claimed that it was late. But your question does not contain any indication that you have any evidence to this effect. On the other hand, you can't appeal a rejection because you weren't as well qualified as some other candidate -- your "appeal" in that case ought to be to get more experience and more education so that on your next try, you are better qualified.