I think you're conflating religious beliefs with ethics. You can't have a religion that is flexible on beliefs, otherwise it is not a religion, but the actual core religious beliefs are fairly limited. In Christianity, Jesus dying to reconcile the world to God is the whole point; without that it is something else. The whole point of Buddhism is that all emotions are pain, and that realizing that everything really nothing (since all composable things are impermanent and everything is composed) is the path to nirvana. All the other beliefs and ethics come out of this.

But even "submarine" religions (ones that people do not think of as a religion) follow the pattern. Communists worship the State (or perhaps the Party), because the problem with society is the structure of society, so only the State can bring the salvation of equity. American Progressives worship sexual identity. Progressives are flexible--except if you don't accept a particular identity, think that gender is not malleable, refuse to use pronouns, etc.

However, I think even "most religions" are not very flexible. 50% of the world's population are either Christian or Islam, and both are pretty prescriptive in the ethics.