On my turn I attack a BF, opponent plays Hidden Hostile Takeover. After Hidden Hostile Takeover resolves, they attempt to sacrifice my unit on an open showdown. Is this legal?

Yes, this is legal.

After Hostile Takeover resolves and the chain empties, the Showdown goes to Open State. Since the chain was opened by a played card (not a trigger or Add ability), Focus passes to the next player — your opponent — per Rule 346. With Focus in Showdown Open, they can play a card with [Action] or [Reaction] timing (such as Hidden Blade, which has Action) to kill the unit they now control.

This is directly supported by FAQ #8808 and #9563 — you can Hidden Blade a unit you took over with Hostile Takeover, and since you control the unit when the kill resolves, any "controller draws" effects (like Hidden Blade's draw 2) benefit you. The same principle applies to any similar kill/sacrifice effect with proper Showdown timing.