There's likely no way to ask this without sounding dramatic. Governments rise and fall all the time, no one is immune. I do not personally know anyone that has lived through events similar to what's going on in the US right now so I am unprepared if the destabilizing events happening in the US right now keep escalating.
What can I do to prepare myself for potential further instability?
As Chomsky pointed out in Manufacturing Consent, modern-day propaganda isn't about lying or faking data, that's pre-War stuff. Post WWII we discovered that a much better way to manipulate public opinion is to focus on some data and not focusing on other data. Omitting that which doesn't match narrative, and headlining the stuff that matches narrative.
Believe it or not, it helps to stabilize you. As Taibbi points out, the news media has turned itself into market segments, where a news story is decided upon, "Will my market want to hear this" and NOT "People should know this." Therefore it's intended as outrage and anger by design. Once you know this, you can take a step back.
That's the psychological preparation.
Several people below wrote "community" and "social group." For those of us in cities and not small towns / farming communities, that translates to "make some friends" which isn't really that useful advice, I'm afraid.