Why are publicly funded institutions allowed to
decide who's opinion matters and whose doesn't?
At a very minimum, there are real-world constraints at work.
There are a limited number of lecture halls and auditoriums. It costs money to run the facilities. Staff is required to maintain them. Somebody has to sweep the floors. There are heating and cooling bills to be paid and new boilers to be purchased every few decades. There are a limited number of hours available in students' academic careers.
A university cannot provide platforms for an unlimited number of professors and guest speakers; a student cannot attend an unlimited number of talks/lectures.
Therefore it is obvious. Choices must be made. One could even say that this curation is one of the most elementary duties of an educational institution.
What's your alternative? Should publicly funded institutions make zero curatorial choices whatsoever? Should literally anybody be able to teach there? If that is not your position, then you surely accept that some curation needs to occur.
This is not incompatible with the wishes of the people nor does it suggest that educational institutions should have dictatorial carte blanche. They must make choices, but must also be accountable to the public.
Are we trying to curtail freedom of speech?
No.
Nobody is arguing that the subject of the linked article should be barred from expressing her views. This is strictly a question about who should (or should not) be obligated to give her a soapbox and a megaphone.
They shouldn't be allowed to take a stance
because they are the government.
There would be considerable benefits to getting the government out of the education business entirely. The downsides would be considerable as well.
It would be worth looking for examples of times and places when government kept its nose out of education entirely. I do not think you will enjoy the correlation between "governments disinterested in education" and... well, anything good.