As a current Yalie, I can say that Yale is no less conservative nor more liberal than other top colleges across the country (Harvard, Princeton, Stanford, etc.) It draws its students from pretty much the same pool of applicants as nearly any other peer university, and I fail to see how the political climate on campus is markedly different.
The Yale Daily News’ article needs some clarification as well. A distinction needs to be made between being a conservative and being a outspoken Trump supporter. Being a conservative/libertarian here will not make you part of the majority, but your views will still be considered, respected and listened to if conveyed in a thoughtful manner. There are lots of conservative events on campus, and a lot of conservative alumni in prominent positions (the 2 bushes, William F Buckley Jr, etc.)
What a lot of Yalies do have an issue with is someone being an outspoken Trump supporter, primarily because it has connotations of being racist, misogynist, Islamophobic, etc. Even then, your views won’t be muzzled, they will merely be rigorously challenged, ignored or met with an ‘eye-roll’ reaction. For instance, there was news recently of Milo Yiannopoulos (editor of Breitbart news) being invited to speak. Most people I knew merely planned to ignore the event, debate the speaker, or attend another opposing talk outside the planned event.
Ultimately, I think far too much noise has been made about this whole issue. An overwhelmingly vast majority of college life and academic research, whether it’s doing p-sets, conducting research in labs, writing plays, curating museum exhibits, or having philosophical discussions, is barely ever politically contentious and even more rarely infringes upon the ‘grey area’ of free speech. This is a non-issue and one that you should barely consider in your college search.