This is a real thing that happens; for example, Robert Bowers, who shot up a synagogue and murdered a bunch of people in Pittsburg a few years ago, was very sociable with other people who shared his anti-semitic beliefs. Eventually he got sick of complaining and other people saying 'there's nothing you can do it about/you'll never do anything about/don't do anything about it yet, wait for a 'better' time.'
Although there's a popular trope about 'lone wolf terrorism' some researchers are starting to argue that it's a bad caricature and that many ideologically-motivated mass shooters have social support of one kind or another, as discussed here: https://www.researchgate.net/publication/321955758_End_of_th...
Of course, most people with ideas we consider wrong are very unlikely to be future terrorists. But they can end up having a significant impact on policy by voting and donating. So if you care about, say, the environment you have quite a strong motivation to argue online with people who say that climate change is not a big deal, and so on. It's not too hard to think of examples of this from around the political spectrum. Universal communications technology that allows us all to talk with each other at near zero marginal cost has brought conflicting worldviews and values into the sphere of public debate and depending on the stakes and the degree tow hich said values make up people's identity, the discussions can be very bitter.
It's important to remember that a great many people simply don't have the option of ignoring people who are wrong. You could be walking along minding your own business and suddenly find a complete stranger harassing or even attacking you because of some bias or bigoted worldview they hold. Sadly, this is not unusual.