Remember - one way to get three cults played against you is if one person plays three of them. ANOTHER way to get three cults played against you is if you're playing 4-player and three people just play one cult each.
Played singly, it seems like an extremely high variance version of cutpurse. Cutpurse makes your opponent DISCARD a COPPER. Cult would make your opponent TRASH a SILVER - much stronger, but also very swingy (and of course it could also do the same thing for Villages against an engine deck, and so on.) A
In a four-player game, the second person in a row to play Cult would have already seen the hands of two of the players (if the previous Cult was a miss), and be guaranteed to hit with it. (This CAN be political - if you've seen two players' hands, you get to choose which card to name based on who that will steal from). Compare to Pillage, also, that can discard targeted cards, this can trash targeted cards (but only up to Silver).
Also, compare to rogue - it takes 2 plays of rogue to trash an opponent's card and dig it out of the trash, and most of the time you're grabbing Silver or something like that anyway.
It creates an obvious pin - an engine with cost reduction can destroy the other person's deck, no luck involved. With even one or two highways in play, you can destroy all of their engine components, and then destroy their provinces at your leisure, it's not like they'll be buying any more!
I think this is a card which would cause a lot of frustration at times, but not have the corresponding "hey, this is awesome" moments to make it worth it.
Trashing attacks are hard to do right, Donald X has talked about all the hoops he's jumped through to make stuff like Knights work out. I don't think that Cult is there yet. This one is a discard attack AND a trashing attack AND a gainer for you at the same time...
I do like Mob though. It's a peddler variant - it gives +1 Card, +1 Coin, and sort of a fake +1 action (if all you're doing with that action is playing Mob. ) Or you can think of it as a weaker conspirator variant - if you activate it by playing a village first, all future mobs are nonterminal-like. Maybe phrase it as "If you have a mob in play, this does not take an action to play"? Or "while this is in play, Mobs do not take an action to play"?
I do not expect that Mob would be OP. It would be very good in games with +Buy AND spare +action... well, the same times that regular Peddler probably gets down to $4 or $2 or even $0 pretty easily! And peddler isn't at all OP when you just use it for its on-play abilities rather than with Trash for benefit.
If playtesting reveals that Mob is indeed OP, you can make it weaker by just raising the cost to $3, but it might be too weak at $3? And hey, I think Mob might be a great candidate for another $1-cost card like Poor House. Upgrade/Remake your coppers into mobs! Anyway, I think there's no way besides playtesting to decide whether Mob is best at $1, $2, or $3, though $2 does seem like a good start.