Parliament, like universities, has traditionally been a place where any and all proposals and ideas are discussed and debated. Not unlike universities, Parliament considers all sides of a debate. It then makes its judgement based on the merits of each argument. But Parliament is allowed to no-platform speakers.
If parliament is allowed to reject speakers for their opinions, then so should universities be able to. Donald Trump was denied the privilege of addressing Parliament on his recent state visit to the UK on the grounds of its opposition to racism and sexism.  If Parliament can reject a speaker because the members of that Parliament reject the speaker's racist and sexist ideas, why can't a university express the same rejection of a speaker's ideas?
Parliament rejecting a speaker is not the same as a university rejecting a speaker. Parliament does so as a political gesture. Bercow barred Trump from speaking as a gesture of protest that the House of Commons was opposed to his Muslim ban. Universities are not there to make political statements, they are there to further human comprehension and understanding. They are also there to educate students and inspire. These roles demand that universities engage with a wide range of ideas to ignite healthy debate, challenge students, and enhance human progress and understanding.
P1: Parliament and universities have a similar role. They both are spaces designed for the healthy debate of ideas. P2: Parliament can no-platform speakers. P3: So, universities should be able to.
Rejecting the premises
Rejecting P1: Universities and Parliment have different roles and different functions.