Are you sure other people are questioning your ability to read? Why do you think this is happening?

This is unusual.

People ask you if you can read? In a serious conversation, not like, "yes we're open, can't you read the fucking sign?"? I think you just say, "yes."

This is the appropriate response.

Ask them about the books they've read, and see if you can find one you have both read

Have you tried writing them a text? Being able to write without being able to read would be weird af if it was even possible.

Talk to people about books you've read