How normal is it for someone working in test automation for 4+ years to ask how to install an intellij plugin via screenshare and accuse me for being impatient and rude for suggesting them to google?

Don't know. On the rare occasions when I've had to touch Java I could kind of feel bits of my brain dribbling out of my arse, so it could be quite normal.

Not very normal I’d say

Maybe he tried and failed and needed help with it. We probably all needed help with a very basic problem that is too obvious for some people.

Heck, my ex-boss admitted he recently learned how to peel potatoes and he is nearly 50.

It's not normal because:

1) 4+ years experience

2) Computer Science specialist, so task is too simple. A tester likely has had to deal with many framework testing plugins and frameworks (e.g. Robot Framework), let alone a simple IDE plugin

3) Should be more professional and graceful

4) If it is an exception, then perhaps we can make an exception, but again, as a Computer Science specialist, troubleshooting is part of the work

No clue whether this is normal, but 'have you tried googling it' is a very sound advice. Some people just want to be spoon-fed, though.

It isn't rude to slap the google
I hope it isn't

Seems pretty common in my experience. The amount of folks that jump directly into asking others for help after trying literally nothing themselves is astonishingly high.