I was most definitely brought up in a Working Class family, and we are all shoes on. In fact i've never been to a shoes off house. It wouldn't even enter my head to offer - not because i'm rude, but because I genuinely have NEVER come across a shoes off household. However, if I went in to someone's house and their lounge (or area we were meeting in), had cream carpets, I would ask. It's common sense in that situation isn't it? If asked to take my shoes off I wouldn't find it a problem at all, unless it was cold, draughty, hard flooring. I get very cold feet, but I wouldn't say anything.
We have wooden floors throughout the downstairs of our house - well upstairs too (apart from tiles in the kitchen and bathroom). The only place we have carpet is on the stairs.
We have friends who when they come round always take their shoes off, I still can't get used to it, but if that's what they feel comfortable doing then that's fine. They know it's ok with us if they leave shoes on. Their own house isn't a shoes off house.
If you can't be comfortable in your own home, then where can you? I think that when you go into someone's house you are entering their space, so I would do as asked (this is just MO). Obviously disabilities excepted.