Indeed, when I took statistics in college, nearly 40 years ago, we proved Bayes theorem, and worked through several applications, so it could hardly have been regarded as controversial.
The controversial part is the methodology for statistical analysis built on top of it (e.g., you need a prior but where did that come from?)
It is ultimately the same math, if you are comparing apples to apples. Just different ways of looking at a problem. Sometimes one is better suited than the other.
It’s like as if physicists were arguing over whether Cartesian or Polar coordinates were better. It’s the same damn physics, just expressed differently. In some problems one approach is easier to work with than the other, and can even make seemingly intractable problems solvable. But that doesn’t mean the other approach was “wrong.”