OK, checking one of my characters, the in-game badge count is 1322. I have the exploration version of Gate Crasher, but not the achievement version.
Sentinel is showing a total of 1322, matching the in-game total.
CIT is showing a total of 1321, one less than in-game and Sentinel are showing. Gate Closer isn't showing up in the exploration list at all, so that's definitely the badge that's missing from my total.
So, if I had both Gate Crashers, I would expect in-game and Sentinel totals to both register as 1323 and CIT to show 1321.
Sentinel not matching and showing one more than in-game still doesn't make sense to me.
Edit: Just to double-check, logging in a rogue with Gate Crasher, I have a total of 1245 in-game, 1245 in Sentinel, and 1244 in CIT.
And I've edited the above text because I should have been looking for Gate Closer on my vigilante, not Gatekeeper.