Ekko revolutionary hostile takeover using ability

It depends on which one goes on the chain first — but if you activate Ekko's ability and they Hostile Takeover in response, the ability still works and Ekko comes back to your base.

Once the ability is activated, its controller is locked to whoever activated it — changing control of the source does not change control of the ability (Rule 191.5.b, same logic as the Rek'Sai attack-trigger rulings). Their Takeover resolves first, takes Ekko and readies him, then your ability resolves: Ekko is banished out of their control and you play him to your base, ignoring his cost, entering ready — "your" in the ability means the ability's controller, not Ekko's current controller. Net result: Ekko is yours at base, and their Takeover has nothing to give back at end of turn.

The thing you can't do is use the ability in response to the Hostile Takeover. The [Action] tag on it only adds Showdown–Open timing on any player's turn (Rule 806.1.c.2) — it never grants Closed-State permission, so once their spell is on the chain you'd need Reaction to activate. So fire Ekko's ability in an Open State (your Main Phase, or a Showdown nobody has added to yet) — and note the discard 1 plus [1][C] is paid up front and isn't refunded either way (Rule 426.1.c).