The right holds, insofar as it is genuine, a scarcity perspective on free speech.
A man on the right says in some setting, public or private or commercial, that he believes some group of people is wrong or sinful or dangerous. Some of the people who hear him choose not to invite him to their parties, choose not to do bespoke business for him, choose not to publish his words in their papers. He feels that his free speech has been impeded. (This has no bearing on the first amendment, because the government takes no action against him, either directly or indirectly. Maybe some people in the government even yell on the telephone at people who choose to publish and amplify his words, but they don't do anything about it.) He responds to this by, once acquiring governmental power, finding people on the left who say things he does not like, sending masked plain-clothes agents of unspecified department in unmarked cars to grab a woman from the street, then revoking her visa, shipping her to another state, and refusing to engage or comply with the courts concerned about the lack of evidence or process of anything.
The man on the right sees scarcity. Either he can say his thing without any consequences (personal, public, commercial, etc.), or the woman cannot say her thing at punishment of unwarned forcible abduction, imprisonment, and expulsion.
The left sees free speech through a lens of abundance.
A person says X. Another person can say not X. Another person can say that the first person is wrong for thinking X, and that he shouldn't be invited to parties. Another person says that X is wrong, but it is wrong to dis-invite the person from parties. Another person says that X is right, if you think about it, and everyone else is wrong. The original person goes to some parties, and not others. Everyone says everything. The consequences for saying things, insofar as there are any, are social and maybe commercial. (Branding is sensitive due to the cost of offending potential customers.) Sometimes the government's representatives say, "We believe X is wrong." But no action is taken. No lawsuits are made, unless the person uses X or his speaking of X to cause external harm.
This is a perspective of abundance. Anyone can say anything, and any consequences are natural and mostly in the form of more speech.
I am an abundance-oriented free speech advocate.
Kanye can say his shit, other people can say that is very bad, other people can say that actually it is okay, and after everyone says what they want to say, maybe now fewer people buy his products and services, because they feel uncomfortable with his messages, especially how they impact his product. If Kanye says his stuff in order to, or with the predictable effect of, someone harassing or hurting someone, then law enforcement gets involved and the laws play out on those who did the thing and those who increased the likelihood of the doing of the thing. All the while in that legal process, there will be evidence, trials, hearings, sentences, forewarning, etc.
That is how things are supposed to work. I will wish some people didn't say their things. Other people will wish I didn't say my things, or will wish people I think are fine didn't say the things they say, etc.
Right now, though, it looks like the position on the right is that if you say something in a student newspaper and take no other action (i.e. if there is no evidence of presence at protests or vandalizing or public speaking or anything), then the government can grab you and take you and do with you what they want, without any explanation or process to anyone whatsoever. Somehow, in the scarcity mindset of free speech, this course of action preserves the limited amount of free speech that can go around, so that some guy somewhere else can go say X, and no one will dis-invite him to their parties, because everyone is afraid that if they say that X is wrong, then they too might get picked up and taken somewhere without cause, explanation, or sentence. The man has finally achieved the freedom to say X without consequence.