I think there's a good in-the-moment discussion to be had here about Containment Priest vs a Life From the Loam/Cabal Pit Dredge deck, but I think it behooves everyone to remember the the metagame changes, particularly the MTGO metagame, and very particularly Dredge hate. The Dredge/anti-Dredge dance seems to move faster than a lot of similar metagame cycles, for whatever reason, and it wouldn't be shocking to me to find the top Dredge players on something else by the time EW rolls around ... or for that matter, next week.
I think it's a pretty great skill to be able to identify where we are in that cycle though, and I'm going to bet you're pretty dead-on at the moment.
In defense of Containment Priest, a card I personally love ... I just want to briefly sing it's praises regardless of Cabal Pit. I'm mostly a proponent of the idea that quantity > quality when it comes to Dredge hate. If possible you want both, but a lot of times you want that deck space for another matchup. Consider the deck that runs 4 Grafdigger's Cage against Oath and Dredge vs the deck that runs 2 Wear//Tear and 2 Rest in Peace. While Rest in Peace is dramatically better against Dredge than Grafdigger's Cage, my money's still on the deck with twice as many cards.
Containment Priest takes this one step further by being the most versatile card you might call Dredge-hate (though you could argue there are some other more versatile non-"hate" "anti-Dredge" cards like Tinker). It's the least-bad Dredge-hate card in many non-Dredge matchups which means the cost for including it in your deck is lower. I've run maindeck Containment Priest in Mentor/Xerox decks before and I suspect I'll do it again. Even outside the Dredge and Oath matchups, I've found Containment Priest winning me lots of games on Ambush Viper duty ... as a Planeswalker-sniper, a surprise blocker, or just a clock during a stalemate. All of this means the card is not so bad maindeck, and 2-3 maindeck Containment Priest has a much bigger impact on the overall Dredge matchup than 1-2 sideboard Rest in Peace
This all feels like it might be pretty obvious to a lot of players ... but I'd just say that I wouldn't count the card out as an option just because of the presence of Cabal Pit, if the next-best alternative is running less for the matchup overall. Versatile cards like Priest and Cage (and Crypt/Spellbomb in some metas, I like the card against storm decks) are a way of creating virtual slots in your deck, which could still be worth it, even if Priest is worse a the moment, the way @wfain predicts (and I think that prediction has merit).
Of course skilled Dredge players know that this will always be true for cards like Priest and Cage, and never be true for cards like Rest in Peace ... which means they build their decks accordingly ... and the great wheel of the metagame rolls ever onward.