Are there any known examples of spurious strong chess openings, which have been determined to be dubious with the introduction of the first engines? I'm curious about the history of chess openings. Nowadays there is a lot of theory about what opening moves are considered mainstream and (near) optimal, such that either side can keep up with their opponent and maintain equality (or an advantage if anyone errs). 

This sometimes goes for up to 25-30 moves without either player thinking much at all, simply because they know the best moves and have studies it extensively, and undoubtedly validated it with chess engines.

Now I'm wondering about before engines were a thing. Are there any known examples of openings, previously considered to be strong or played regularly by strong players, but later -- with the help of engines --  determined to be dubious/easily counterable?
Pretty much any opening that is no longer played was "refuted" by an engine. You can check for example the 9. 0-0-0 Nxd4 line in the Sicilian Dragon. 

Computer analysis has also found interesting ways for White to keep the advantage in the From's gambit, although this opening was never that popular (because of 1.f4 being a rarity)

About 25 years ago, Kasparov reintroduced the Evans gambit into elite chess. Despite initial success computer-assisted analysis forced it to step away again.

The list goes on and on, but sometimes it's just about a variation in a particular line being changed by another, rather than something like the Sicilian or the French being abandonned altogether