can kwickset and gatehouse knobs be rekeyed to match

No. You cannot rekey. But this lock set doesn't have a key anyway. It has a switch on the inside.

To answer your question, yes, Gatehouse and Kwikset locks can be re-keyed the same. However, the lock that you asked the question on, is not an exterior door, and does not come with keys.

Yes. Current Gatehouse locks use a kw1 keyway. This is the standard keyway for Kwikset as well. The difference between the two is that most Kwikset lock have the ability to be rekeyed by anyone. Gatehouse does not. Gatehouse uses classic full metal construction on every door knob and deadbolt. (With the exception of the electronic keypad deadbolt.) To get the Gatehouse locks to match kwikset keys, take the old keys and the new keys, as well as the Gatehouse lock to a hardware associate in Lowe's, and they will be able to rekey it for you.