I've never had a problem with muriatic acid eating plastic. heck, I've used it straight to clean stubborn deposits off of plastic, both tank frames and hood/lights. Sure you're not thinking of acetone or lacquer thinner? Muriatic acid comes in plastic jugs, BTW, and i don't think they are any 'special' plastic.
if your stains are on the outside of the tank, you could use lime-a-way and just wipe off when done.
MsG: If you do use muriatic acid (aka HCl or hydrochloric acid) be very careful and dilute well, start with 1:10. That usually is plenty strong enough for most things...and use gloves!
ALWAYS add acid to water never the other way round.
I had a 10G tank that was REALLY limed up inside, as was the HOB (plastic) filter. set it outside, filled it with water and 'one glug' of muratic acid. ran the filter for a week. filter and tank were beautiful.