I wonder what would happen if you had a solid piece of antimatter, say a gram of anti-iron... and just set it down. Would it really annihaliate immediately on contact with air, a lab table, or anything... or would the normal forces that keep us from falling through things still be in effect?

Either nothing would happen, or like molten salt in water, the joule currents would be instant and drive it all to go boom in a big way. I wonder which.

The charges are inverted, so anti-protons are actively attracted to protons.

It would immediately explode.

I think OP is proposing a lump of antimatter with no net electric charge.

My guess is that even in this case the lump’s positrons would immediately interact with the table’s electrons and explode.

Even without charge attraction, say anti-neutrons (I don’t know the term) would instantly resolve because neutrons are everywhere.