Having come into caving from climbing, I've always thought it's quite odd that cavers are so adamant about rigging on locking carabiners but then use snapgates as their primary attachment.
There's no good reason why using snapgates in rigging is 'dangerous' in general. Usually it shouldn't matter if any single anchor fails, because we normally expect that bolts _could_ fail. So if a rigging snapgate opens and the rope pops out (which is pretty unlikely, really, due to how they are loaded), that _shouldn't_ matter beyond a small drop and a requirement for new underwear.
If the rigging is crap and you have to rely more than you would like on a single anchor, then use a snapgate. I don't just mean a single-anchor rebelay, because as long as there is a reasonable bit of rope above you (for shock absorption) and nothing below you to hit (i.e. no ledges and ideally this isn't the last rebelay, which is better with doubled anchors) then it's still generally fine if the anchor pops (provided you are using sufficiently robust ropes that you won't destroy them immediately on an edge or something).
Equally if you have used a single bombproof thing (like a massive tree) as your anchor and haven't doubled up on slings, for example, then obviously you need a locking carabiner on it. You also need to be more careful about clipping into snapgates with your cowstails (probably better to clip the knot).
Whereas cowstails carabiners are constantly in use, often end up in weird orientations as you move around, and are likely to be sliding along ropes which also increases the risk of unclipping. I do not have time in my life for screwgates on cowstails, however, and I suspect a lot of screwgate cowstail carabiners are rarely done up. I have Petzl and DMM twistlocks which are fine; I also have a set of Petzl Vertigo via ferrata carabiners for the Dachstein mud where it is hard to grip your twistlock gate.
When we went to the Berger last summer (which the French had rigged as we were just before the international camp) the occasional snapgate deeper in the cave did alarm a few British cavers...