Rules
Probably what happens when we read anything from history nowadays.
Some people will look at the source critically. 'Was Suetonius trying to pander to the powers that be when writing about the Julio-Claudians?'
Some people will take it as gospel like people do with the whole 'CORSETS WERE EVIL!!!' discourse because they saw a few satirical pictures making fun of women tight lacing (which wasn't actually common btw).
Same as it's had throughout time
We're already there, so look at the present.
Further fracturing of reality. More and more unique bubbles that people live in beyond left/right, pro-vax/anti-vax, etc. It's hard to imagine exactly what this will look like, but I imagine even more distrust, stupidity, anger, cruelty, and violence. Have a nice day!
Propaganda, election meddling, manipulation, scams, war, genocide, civil war, etc. Nothing new then, so please, carry on!
On a certain level, it's not the lies that have changed, just the ease with which they are shared. People used to write up their views from outside consensus reality and have to go give them to people one at a time, first talking, then writing, then printing, then radio, then TV, now with all the speed and convenience of the internet.
It's hard to say how the majority of people will handle it. I doubt most people will be able to adapt to such a noisy information environment. Something has to simplify it for them. But I can't predict at what ratio it will be between sanity-preserving self-imposed ignorance, government censorship, cultural censorship, curious confusion, crowd-sourced information bubbles, or elements I haven't even thought of. The only thing I can say for sure is that it won't be stable.
Why would that change? Think of modlogs and the fact they were supposed to dispel lies but ended up championing them. Think of what you believed about others and what you still believe. Or not.