Ribbon Tweeters and Animal Hair

"Always keep pets away from delicate gear. A good blast with pressurized air for cleaning on occasion sounds like a good idea to me."  Mapman

Not sure my dog would go for that.  But I guess it would teach him not to go near the hi-fi.

Hello,
Cats really dislike aluminum foil and sticky stuff. You can use it to deter the cat from getting on top of the speakers or around them. The real issue is keeping them clean. See if you can figure out how to clean them. Also, I would add a hepa air filter in the room. You might have to turn it off while listening but it will cleanse the room while music is not in use. Also, Another wired one. Put fly tach strips or double stick tape near the speaker. It will grab and hold everything. Good luck. 

My last system was Ascend’s Towers and Horizon Raal with Sierra 2’s as surrounds. We have two Australian Shepard’s and never had any problem. I loved that system. I stepped it up To a Legacy system now but those Ascends were sweet.

Cats will use the grill cloth as a scratching post. They will not bother the drivers. You can get electrified plastic mats that you can put around the speaker. Any biologic organism that steps on the mats will get an uncomfortable buzz just bad enough to relate to that organism that this is a no go zone. You keep the mats there for 6 months and you can remove them.
If the speakers are cool looking with the grills off then keep them off. Pet hair is heavier than air. As long as the pet is not above the speaker hair is not an issue. Ribbons can be very delicate, you never want to vacuum over them or blow into them. You want to keep a spare ribbon in hand in case something happens. You wipe the speaker gently with a damp cloth.

I would always keep the grilles on just to be safe especially with children or pets around the house it is better to be safe than sorry and a lot of speakers are voiced with the grille on.