If my opponent is using the Dark Depths & Thespian's Stage combo, am I able to respond to the "When Dark Depths has no ice counters" trigger with a Stip Mine or Boseju and prevent them from making the token?
Related question, if I have a Stifle, can I counter the ability to make the token after they have sacrificed both their lands?
For those who don't know the combo, I'll explain it step by step:
The first step is to activate Thespian's Stage to copy Dark Depths. When this ability resolves, Thespian's Stage becomes a copy of Dark Depths, but one without any ice counters on it (since it didn't enter the battlefield as a copy of Dark Depths).
Before any triggers go on the stack, the game checks state-based actions and sees that a player controls two legendary permanents with the same name. To rectify this, they put one of them into their graveyard. (In order for the combo to work, the original Dark Depths must be the card sent to the graveyard here.)
Now we put the Stage/Depths's "no ice counters" trigger on the stack. This is a relatively normal trigger and can be responded to with abilities like Strip Mine to destroy the land. Countering the trigger with Stifle won't do anything productive, however, since the state trigger for no ice counters will just trigger again once the first iteration of the trigger leaves the stack.
When the trigger goes to resolve, the Stage/Depths will be sacrificed (if it's on the battlefield still). If it was sacrificed this way, then the Marit Lage token will be created. This is all a single trigger with no opportunity to respond to anything between the sacrifice of the land and the creation of the token. (If the ability was worded "When you do, ..." rather than "If you do, ...", it would create a new trigger for the rest of the effect, but Dark Depths well pre-dates that templating technology.)
The net result here is that both lands are in the graveyard and a Marit Lage token has been created. The interaction points during the process are limited due to Dark Depth's ability being both able to re-trigger if countered and being only a single trigger, leaving no way to stop it once both lands are in the graveyard.
Of course you can always just bounce or exile the token...