It really depends on my mood, and the level of bullshit being spewed.
Since I no longer care about whether people like me or not, I have no trouble with telling anyone they're full if shit.

A co-worker started texting me regularly. Many texts use to have religious suggestions. After about 4 years, he is my best friend. But the texts arn't religious anymore. But I didn't just plainly ask him to stop with that. I asked thought provoking questions. When he suggested to please God, I asked, "how is God pleased?" He replied with the pat answer of the commandments. But it eventually occured to him that I am not religious and he dispensed with the religious stuff. And I did not have to seriously offend him.

Kindly, curiously, persistently, I ask them follow-up after follow-up question until they run out of BS. I then just shut up and wait for them to figure out what just happened.

And that's if I like them.

I am a science educator and have the same problem. I try to date and have problems getting through the first one. They usually believe in something crazy and won't keep it to themselves. The last one was a climate science denier. I do have friends who believe crazy things and keep it to themselves. That's OK as long as they don't expect me to listen to it.

When a friend posted some anti-vaxx BS on FB I called her instead of having a public debate. Calmly I explained the history of the disproven, falsified study that started the movement and the risks to her child. I told her that my information came from a college microbiology class I took a few years ago, not the web and backed up the information with weblinks to the World Health Organization and others. She took down the post and vaccinated her son.

I research and share information, I don't put energy into "converting" or "informing" someone else. Most can only comprehend based on their level of intelligence and cognitive bias.

While I disagree with many, especially brainwashed lower and middle class Americans who religiously vote Republican. I don't unfollow them or don't listen to their point of view.

I have learned to listen to another's point of view, disagree with it and move on.

If I care about the topic (not their misconception) I may counter by asking questions which seed doubt into their narrative. Show results or conclusions based on the topic at hand.

It is what we do, not say that matters. I feel the same with topics online.

Most of the time however, when deciding to expend energy in informing a misinformed topic. Those spouting it will eventually just shut down and or dismiss anything that doesn't support their existing narrative. Even if the counter to the narrative is double or triple confirmed by independent sources.

Agree to disagree and follow your own path.

Biggest problem I've had is with old co-workers. If they violate the boundaries, I walk out/away. In social settings with friends acquaintes, i try to put my opinions out there.... If they are unwilling to accept my words while insisting i accept their's, i pay my tab and leave. It may be childish - take my ball and going home - but for my peace of mind, i can't have it stress me out. If i'm entertained by the speaker, that's a different scenario. But bothered, i get out as soon as i can. (But i have no job and no friends, so.... Um... Maybe im not the best to give advice.)

I like the line, “I’d like to see the double-blind study on that.”

Sorry I'm not a scientist so I can't give you any advice. If I was a scientist I would suggest giving them the truth and showing them how they're wrong. That goes over really well on this site where people will call you a troll because they don't like your answer and they can't back up their argument. If you don't want to stand out in the crowd you just have to grin and bear it. Or something like "you might want to check your sources on that" and then leave it alone

I've come to accept (to some degree) that it isn't my purpose in life to correct all the bullshit that makes it into my orbit. I'm a high school teacher, and it can be damned hard in class to correct nonsense that only touches on my subject area, but I find myself correcting a few things outside of my area when the need arises (and when I am the least bit unsure, I say so, or tell students to ask the appropriate teacher...or if it a simple fact I do not know, I google it). That's WORK.

We don't get paid to correct nonsense around us 24/7. And we'd drive ourselves crazy just attempting it.

Casually ask for their sources first. Then casually indicate how strange it was that you saw the opposite in [name your reliable source]. Not confrontational and fact based.
I do that all the time.

In social settings I mainly say “OK” or “if you say so”. Sometimes I will ask questions about it depending on how well I know the person.

Stop taking other people’s opinions so seriously.

There's lots of BS out there and many take it seriously. I knew an Engineer once who believed he helped build the pyramids. Just the other day I saw a person looking on the Internet and claiming that a woman in labor was going to get an abortion. In hindsight now I wish I would have remarked "tell her she had better hurry up."

Good scientists enjoy being proven wrong. They relish it...especially if your proof is detailed or documented well.

Pseudo-scientists espouse lots of info but rarely "cite" their sources. They come on as "know-it-alls" and instead of telling you sources, they'll put the onus on you to "prove me wrong".

So to answer your question of "How do you deal with people in social settings that speak with authority..."

I reply;

"as a teacher, I constantly reminded my students that "being a scientist" is a state of mind...not a paid position.

If you are a calm skeptic....not rude, not arrogant...you just quietly demand the facts and evidence - you're being "a scientist". If the person espousing the information is reluctant to "show proof" then you've won the scientific debate; you're being the scientist....they're not.

[americanscientist.org]

Stick to your guns and hope for the best. I believe in humanity but individuals' ignorance is sometimes staggering.

When it comes to climate science (the denial thereof), because it is an imminent existential threat, I will go to the mat every time. On other, more philosophical topics, I pick my battles.

You can always ask them where they got their degree from? What I really hate, is when you've just corrected somebody's ignorance, and someone says "Oh yeah? How would YOU know?" (To which, I can only respond "Oh, I READ a lot!" ).

I ignore them and unfollow some

Live and let live and strive to do or cause no harm.

You have come to a largely crap free area here, you never know with luck you may find a friend or two. You don't really need that many, it is quality not numbers which count.

I'm the last one to ask. I still like being right more than being liked. Fortunately, I sometimes find people that are so full of it that I don't want to bother correcting them. I just passively move on and avoid them.

It is important to keep these dialogs going and not always jump to unfriend or block as the flow of factual information influences some who deny and arms others who do not with stronger arguments and also confidence that they are not outliers. It is difficult and sometimes demoralizing but absolutely necessary.

Back when I was a little confused on Capital Punishment, I wrote Amnesty International that I was going to leave them over their opposition to Capital Punishment (I was 22). A week later, the frickin President of Amnesty International called me and we talked for almost 30 minutes. He asked me my top 5 reasons to be in support of Capital punishment and he calmly, dispassionately, and thoroughly explained the reasons why my top 5 were actually misinformed or not fair assumptions. Totally won me over. But I'll never forget his dedication.

Europe?

I moved to Canada for a couple of years, mostly Toronto, and the people there are honestly much kinder and open-minded than the US.

That having been said, your big blue cities are better bets for scientific minds IMHO.