How bad is getting tagged as a scammer on Steam?

You will have trouble if you get reported few times... Just once won't do anything

He must provide proof. If no such thing exists, you're safe.

Probably just a rage kid, just ignore him. Reporting for scam without an actual scam won't do anything. Once one of these kids negative rep me because he didn't liked my offers.

Some ppl are dumb, once one added me and started spamming "I need tf2 keys and cards I have games to trade" and continually requesting trade window, without explaining anything even what he has and I never asked to trade for anything, he continued doing this even if I didn't accept his trade requests and tried to talk to him, so I just blocked, but seems sometimes these ppl get mad like in your case.

Nothing will happen, unless he's the type who makes multiple alt accounts and then reports you to Steam.

Then whenever you trade the old "this user has been reported for attempting scams" thing will show up, although if you have a clean SteamRep and explain it most of the time people will be nice to you. Also, contacting Steam might help if this happens. For now don't worry about it.