I only have my chow chow these days and he doesn't seem to mind them. Especially when he gets to go on the road with me.

Yes they do, Mrs and 2 kids age 11 and 13. My 13 year old plays drums and we've covered a few Stones songs, mostly 60s Jones-era ones. We covered Doom and Gloom at a gig about two weeks after it came out. One of the rare times we played anything not from the 50s/60s.
Having said that we all prefer The Beatles and my kids liked The Monkees better than both of them for a while until I offered to feed them again and restore Wii privileges if they admitted they liked The Beatles better. That's Beatle fans for ya.
To their credit, they both hate Davy Jones so my parenting skills appear to be ok.

My Dad was a Beatles fan (he's 72)...he told me he'd always found Mick Jagger repulsive back in the day, so that must be why I subconsciously gravitated towards them as a teenager in the '90s.

wife and son : YES !!
sisters and mother : they couldn't care less

Very casual fans, but yes.

Went with my wife to see the Stones in 1989, 1984, 1997 and 2013. Took my son in 2007 and 2013.