I've argued with one of my relatives on Facebook more times than I care to admit. Plain and simple: They can't be reasoned with. I routinely present stats, data, and evidence of all sorts and their default response is to claim "fake news" or to deflect with all manner of logical fallacy, including the all too common "whataboutism". It drives me insane that they can't argue rationally. It also doesn't help that all of their sources include either Fox News or some far-right clickbait news site that will usually omit important details or include images that have nothing to do with the article itself.
One specific issue I have a big problem with is that they are quite hypocritical when it comes to health care. Premiums with respect to their small business rose significantly due to the ACA. Yes, that sucked, but it's a part that needs to be fixed. At the same time, they still had their 4-5 bedroom house; they still had a successful business; they still took vacations to Hawaii or Mexico every year. They Hcompletely ignored the fact that millions of other people were finally able to afford health care. They comes out as staunchly against universal health care, but since turning 65 last year, they now rave about how cheap and great Medicare is compared to previous years without it. I really want to ask them how that socialized health coverage is working out, but I suspect I wouldn't get an honest response.
I've read various articles explaining that for arguing in situations like this, it can be beneficial to just start asking them why. Why do they feel a certain way? Why do they think X law should be passed? Why do they think it's good? What benefits will this have? I know how it might affect you... but how will it affect other people, and do you care? In doing so, it *might* make them realize that the other guy actually has some reasonable points and it *might* get them to recognize that in some cases they are wrong, hypocritical, or whatever.
One of my friends is a climate science denier. This one's a bit different in that he refuses to argue with me because he would simply dismiss any info I throw at him. At the same time, he'll throw back "evidence" that climate change is a hoax because of the Medieval Warming Period and similar events. He completely ignores that these events were regional and had little to no effect on global climate. I don't know if he understands variance within trends and things of that nature.
So yeah... frustrating.
EDIT: And after all that, I agree with Mercane (above). Eventually, you realize that ignoring them is much more productive and stress-free.