the grills

Some designers factor grill into sound of loudspeaker some suggest removing for best sound. As far as protection most grills will not stop a lab or Child or from pushing in cone. But it does keep it out of site and with kids out of mind. With dogs as long as it doesn't have a smell they like you should be ok. My dogs love the smell of certain drivers they do not damage. But they approach to smell which means press moist noise against cone if you let them. And I don't. My cats where harder on my loudspeakers than any child or dog. Thus today no more cats.

I keep mine off.

I do have a Bernese Mountain Dog who chewed through my $5k Crystal Cable speaker cables...:)...and chewed up my Logitech 1000 universal remote... Still love her...

My cats used to use the exposed label edge of my stored records as a scratching post. The sleeves took a beating but the contents survived luckily.

I keep them off, but I can't hear a difference either way.

I like to leave my grills off, I find they use too much gas when kept on. It only takes a minute or two to warm up, not like the stereo which takes 15 or 30 minutes.
I do leave the grills on the speakers, can't say I notice a difference with or without.
Oh, and we have a big black and white cat