It's been a while, since I've really looked.
But, IRRC, All Tide Liquids, not labeled HE, do or shouldn't contain suds suppressors.
As for Tide Powder. I think, almost all the "Ultra" Powder variations contain, suds suppressors, including Original Tide. The Tide HE variations, however, should contain a another special ingredient, that helps to capture dirt better *usually borax* but since, Tide Powder contains Soda Ash, or Sodium Carbonate, it's not really needed.
If in some miracle time wrap store, you find, non-ultra Tide Powder. The product should not contain suds suppressors, and will make lots of froth.
Keep in mind, you should always try to use HE labeled detergents, however, with careful dosing, you can normally get away with using them, if careful. I'll have to post more about the Tide & P&G powder line later.