Check your antivirus/firewall settings and logs; that sounds like it's interfering (i.e. mishandling the PvP packets) causing the game to crash. By the way, do the crashes get logged somehow in Windows?
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I couldn't find any concrete evidence but I did check both antivirus logs and windows logs and found nothing obvious, but there's a log type that has something to do with BattlEye that props up on the anteater error. Thinking a potential battleye error could be causing it.