I'm not sure why that is relevant. So the congress allocated taxpayer money to schools because they believe(d) that higher education is net beneficial for the country. Whether because it attracts the most talented immigrants from around the world (who typically stay in the country and tend to be some of the most talented workers/leaders) or perhaps for research purposes as many of our military and scientific breakthroughs happen in these universities. The reason is irrelevant, all that matters is at some point congress decided there is a net benefit to the country to invest in universities and up to today, all subsequent congresses reauthorized said funding (they could have repealed it).

In a similar fashion, congress also authorized funds to provide in the form of grants and loans to Americans who would like to pursue higher education.

Now, the executive branch, has decided that they do not like students (paying customers of the universities) expressing their first amendment rights about a particular cause (related to a foreign country). So the executive branch both directly and indirectly stopped these students from expressing their views and violated their first amendment rights.

And the argument is that this is OK because the students are partaking in a system where they did not pay for 100% of their college costs?

By this logic, why can't the federal government tell you that the "Fuck Biden" sign you put in your yard must be removed because the government (fannie/freddie etc.) own or backstop your mortgage? Why can't they tell you to remove the "Fuck Trump" bumper sticker on your car because they paid to build the road your car is driving on?

I can't understand why one would argue for greater government control and for taking away first amendment rights. I imagine this is a partisan issue for you and that is how you reached your viewpoint? I would imagine you'd feel differently if it was your speech that was affected in the same manner or if it affected a cause you cared for.