Mockery is not peer pressure. Peer pressure is the phenomenon in which people feel compelled to conform to the examples set by people they see as peers. E.g. friends conforming to the examples and expectations set by each other. Peer pressure's influence scales with the degree someone respects these people as peers. Mockery usually diminishes that respect.
People who mock each other rarely see each other as peers in the first place, anyway. How often have you seen a BLM activist change their views on police brutality after being mocked? I have witnessed exactly zero instances of this occurring. Same for, say, climate change skeptics. This is because they do not see the people being mocked as peers, and thus do not care about the opinion of those mocking them. This is why mocking is usually self defeating. By resorting to mockery, the people you're trying to influence no longer see you as a peer, and thus it drastically limits what influence you initially had on their views.
You claim that, "when enough people make fun of a particular position, people will avoid taking that position" but I have never witnessed this occur. I have not once witnessed an instance in which a person changed their views after being mocked for them. How many times have you adopted a view you previously opposed because you were mocked? Do people mocking gays or immigrants people make you feel compelled to adopt their views on LGBT issues or border policy, for example? If not, why do you seem to believe that your mockery will be any different in its success (or lack thereof)?
On the contrary, I have witnessed countless people take a defensive stance after being mocked for their views, and entrenching themselves even further into whatever views prompted the mockery. Not only that, it frequently makes people reluctant to take part in advancing the views of the one carrying out the mockery. In fact, this is occurring right now in this comment thread: witnessing you proudly stating that you carry out childish behavior in support of certain views is making me more reluctant to voice support of said views, even though I do agree with them, as I do not want to be associated with people such as yourself that take pride in their mockery.