Can you play an Ambush unit such as Rengar, Trophy Hunter in reaction to Mageseeker Warden entering the battlefield?

Yes — you can Ambush in response to Mageseeker Warden being played, because at that moment Warden is a card on the chain, not yet a permanent on the board.

Warden's "opponents can only play units to their base" is a passive ability of a permanent, and passive abilities are only active while the permanent is on the board (Rule 365.1). So while Warden sits on the chain, you're free to Ambush a unit (Rengar included) to a battlefield you control — or, for Rengar, a battlefield with enemy units — and your unit resolves first (LIFO), landing before Warden ever enters.

The window that matters is after Warden resolves: once it's actually at a battlefield, no Ambush for you at any battlefield, and you're limited to playing units to your base. Note it's a restriction on playing, not on units already there, so your Ambush unit that landed earlier stays put. If Warden is played to its controller's base, the clause never turns on at all.