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Context: Let's say somebody talked to me as if I am Muslim just because of my ethnicity. Can I respond to that person with these sentences? I am asking this because I think the word "if" is probably wrong in these sentences. Should I not use "if" in them?
- How do you know if I am Muslim?
- How do you know if I am Muslim or not?
- How do you know if I am Muslim or whatever?
- How do you know if I am Muslim or anything?
The title of your question uses the form "How do you know I am Muslim?", and that form does not appear in any of your examples 1-4. That form means the same as "How do you know that I am Muslim?", and in effect admits that you are Muslim.
For the other examples, you could use the word "whether" in place of "if". It would be a little clearer in these sentences. Then, I would discard sentences 3 and 4 because they sound a little clumsy.
Finally, for that situation, you might say
"Why do you assume that I am Muslim?"
That would put the burden of explaining the assumption on the other person.