Here's the thing, though, Oregoropa: those people are still allowed to spout their views. Their speech hasn't actually been silenced. That weatherman can still spout his views on global warming and Trump can still bluster and blubber as he pleases. They would just have one less place to express those views. But they haven't actually been permanently silenced.
Also, the weatherman being suspended is the decision of the station he works for, and as a private entity, they have the right to do that if they wish. After all, isn't that the very argument conservatives use when they claim they have the right to deny people service or jobs based on sexual orientation? Pray tell, what's the difference? That's not exactly some example of the evil federal government cracking down on his First Amendment rights.
And it kind of doesn't make sense for someone who is involved in the study of weather to question global warming. If he questioned it, then he's spouting things that aren't true. That's not attacking conservative thought, that's simply firing someone who makes blatantly untrue claims. Why would I want to listen to or employ a weatherman who either expresses doubts about or doesn't believe in the concept of global warming?
As for the college, were they forced to suspend their food night or did they choose to do that? If they chose to do that, well, that was their decision, and again, not really under the umbrella of "censorship". Unless that particular student forced them to shut down their traditional celebration their free speech hasn't exactly been curbed. When the federal government starts actively revoking people's First Amendment rights for these sorts of situations, then I'll take this "erosion of free speech!" hysteria a little more seriously. Until then, this is not exactly cause for alarm. This is a few individuals' personal reaction to what some people say or believe. Again, if you want to say or do something offensive or inflammatory or ignorant, fine, but that does NOT mean you are free of any consequences for what you say or do.
Mind, I'm basing this all on iron horse's simple explanations of these situations without seeing actual links to these stories of these supposed "curbing of free speech" moments. I somehow get the sneaking suspicion that if we were to look up these stories, there'd be a lot more to the reasons why the weatherman was fired, or why this particular traditional celebration at a college rubbed someone the wrong way, and it wouldn't be a simple matter of, "See, look at all these oversensitive people trying to silence others!"
And the UK potentially not wanting Trump to visit has less to do with free speech and more to do with the fact that they probably feel he shouldn't be taken seriously as a presidential candidate. And they'd be right.