[nemo]

>The Christian Church actually said bathing naked was forbidden

There's no "The Cristian Church," I think you're referring to a modern misconception on a Catholic ban on mixed bath houses. They still had bath houses, they just banned men and women being naked in them together. These bath houses were often also brothels, which makes the ban perhaps still prudish, but nothing extraordinary.

Monks did bathe rarely, which is discussed in the article.

While most of the great old public baths of the Roman era closed, there are illustrations and archaeological evidence of bathhouses in the Middle Ages. They're wooden and much smaller affairs, but they still exist.

I recognize a few other common misconceptions of in the rest of your list, and there's a number of issues with "Muslim and Byzantine records mentioned how dirty westener were." There were certainly cases where "Westerners" thought "Muslims" and "Byzantines" were dirty too, that's a standard way to otherize other cultures. Cross-cultural judgments of hygiene are not a thing one should take at face value. But also all three of the labels "Western" "Muslim" and "Byzantine" are broad generalizations. To generalize about their attitudes towards others or bathing is to be in error, as these were neither constants nor universals nor even truly discrete groups.