How much does pickup height affect active pickups?

Active pickups still use magnets and coils just like other pickups, so all of the points you have read elsewhere about pickup height will also equally apply to active pickups.

ceramic pick ups have more of a magnetic pull on your strings while Alnico pick ups have less magnetic pull which will allow you to raise them higher. Active pickup are usually Alnico which will have less pull on the strings. Just raise and lower till you find the sweet spot for tone and response.

I believe active pickups typically have a weaker magnetic field which is boosted by the actiive electronics therefore you should be able to put them close to the string without the out of tune wolf tone effect of passive pickups. Other than that, set them to where they sound good and make noise.

Quote from GLParrishmn

ceramic pick ups have more of a magnetic pull on your strings while Alnico pick ups have less magnetic pull which will allow you to raise them higher. Active pickup are usually Alnico which will have less pull on the strings. Just raise and lower till you find the sweet spot for tone and response.

No. Bridge active pickups are ceramic and the neck pickups are alnico. The only exception I know is the EMG FAT55.