I've been using Cherry Reds for a while now, due to them having the lowest travel distance and activation force of the Cherry options. Recently, however, I've been told Topre switches are superior in this regard..
Is that true? If so, would there be any downsides to using Topres when FPS gaming? My main concern is key presses registering as fast as possible and double-tapping being easy.
Thanks! And happy holidays 
Technically, all Cherry MX switches have the same distance to activation point.
The difference is in the tactility and the strength of the spring. The tactility generally produces a small mechanical resistance just before the activation point, or a collapse just after the activation point.
I have been told that reds and blacks (same as reds, but stronger spring) are good choices for gaming. Browns should not be bad (same spring as reds, but a very subtle tactile resistance just before the activation point). I guess that blues would not be ideal. They are clicky with a tactile point, and they have a small moving part inside which produces the click and which causes a little bit of inertia that may be counter-productive for double-tapping.
I don't see why Topre switches would be superior for games. Not that I think they would be inferior either. They are subtly tactile with a collapse just after the activation point, which is supposed to be at 2mm, and is the same distance as Cherry MX switches.
My feeling is that it's not the kind of switch you use that will make you better at gaming, contrary to what the keyboards manufacturers marketing departments want you to believe.
I think a mechanical keyboard will help, but unless you select a very wrong kind of switch it will not make any further difference.
That's good news: you can choose the kind of mechanical switch you personally like the most.