"I feel like some people confuse having the right to free speech with the idea that I should have to listen to or read it."

Sounds like a straw-man; who thinks this way?

Does the mute function not serve this purpose? What limitations does it have?

Tools to create word filters and your own lists that you can switch between is fine, great even - I can see the benefits of that for giving people the ability to create their own experiences without resorting to using bots to build profiles of people (which may or may not be accurate), when people may not even be aware that this is happening.