Just ask Milo Yiannopoulos or Ben Shapiro what they experience on college speaking tours.
Sorry, but no. Those examples, both, are examples of people speaking not just against some nebulous topic. They’re actively attacking, victimizing, and gas-lighting others, and are often simply being called out on their fuckery by people tired of putting up with them. Anyone attacking others, and then crying or shouting they’re “being oppressed” when the same is done to them? Sorry, not good examples of anything, unless you’re looking for a good definition of “self-hating” or “hypocrite”.
Protesting someone speaking at a university you pay to go to is not shutting down someone’s free speech. No one is entitled to be paid by a college (or any venue) to speak about their beliefs or their thoughts on a topic. If a Catholic Church prevented me from coming in on a random Sunday and giving a speech about the Wonders of Satanism, are they denying my right to free speech? No. No one has a “right” to speak or hold an event in a private venue. If the venue gives consent, and those paying for or funding that venue disagree, they may protest, threaten a boycott, or take other legal action if their status so allows; that’s well within their rights.
Yes, I know, protests have happened in the past that broke laws, in many cases unjust laws. Civil disobedience has a price though, because it is technically illegal. Those doing so generally protest in a planned manner, often with members of both a privileged and underprivileged class, to show unfair and unequal treatment. They also tend to not try to elevate their own status by demeaning the status of others, or demanding that they have a “higher claim” to a right than those that revile or oppress them. Anyone fighting for a cause that puts them above another is fighting an unjust cause. Equality should be the end goal of justice, not dominance.
In summary, free speech has nothing to do with your right to a particular platform. It has to do only with the government, or some other group, not being able to hoist you off to a prison (or worse) for publicly espousing your beliefs. Tomorrow, Medium could ban 70 people for using the word “grapefruit” if they liked. Those people’s free speech rights would not be infringed unless Medium also involved the government, or a militia, and said group arrested, detained, or otherwise silenced those people. That said, people would very likely see such a move as censorship (which is the correct term to use), and as a result move to, or create, another platform as a result. For those in the conservative world, this would be called the power of the free market, which should, in theory, be able to overcome any form of civil injustice, via capitalism. (That, of course, assumes capitalism is itself just, which is highly debatable.)
PS: You may want to be careful about left/right analogies. In different countries, left and right mean very different things. In the US, for example, the right is considered the conservative group, where the left is generally considered the liberal group.