Hazardous Conditions doesn't care what kind of counter a creature has on it. Whether +1/+1, -1/-1, charge, or fate, any kind of counter causes a creature to be unaffected.

The set of creatures affected by Hazardous Conditions is determined as the spell resolves. Creatures that get a counter later in the turn will continue to get -2/-2. Creatures that enter the battlefield or lose their counters later in the turn and noncreature permanents that become creatures later in the turn won't get -2/-2.