[RuggeroAltair]

The issue is not only about mass. Any mass could form a black hole, the main point is about mass density, and that's not trivial to obtain.

That aside, real infinities is a vague concept. What's important is that any theory of gravity has to deal with the fact that the current understanding of classical gravity and quantum field theory make (when you combine them) a theory that has problems at the Planck scale. Those are problems that any theory of quantum gravity or every theory of everything have to deal with.

But it doesn't mean that those potential theories would have any infinities. Such a theory, though, has been very elusive.

With the exception of string theory, which is the leading theory in terms of its success, most theories tend to have fundamental problems. String theory research is certainly not complete, but it's in my opinion currently the best shot we have. Online, and in academia, you can find lots of very opinionated discussions about it, which include aspects of testability, predictivity, etc. which means that some people really dislike string theory and prefer other approaches.