I know this is a Cambridge account, but I wanted to respond to this from the perspective of someone who has studied at a very similar university (Cambridge) and who's worked with offer holders for several years now top hopefully reassure you a little bit.
Firstly, these are entirely understandable things to worry about. It's always difficult to get a true sense of what a place is like until you actually live there. There is some competition between colleges in terms of sports, but it's more like the competition between school houses on Sports' Day. Most actual students (certainly at Cambridge, and I would expect at Oxford too) don't take it that seriously. Colleges develop stereotypes, but they're about as valid as any other stereotype you might come across in life: i.e. not at all. Don't forget that student communities refresh themselves every 3-4 years, so what a college might have been known for 5 years ago is likely to no longer hold true.
Most university-aged students tend to be left-of-centre politically, although all political persuasions will be represented. You'll find people you really agree with, and those you don't. Your college is likely to be fairly small, but you're not restricted to making friends with those people if you don't want to. You'll meet people through your course, through any clubs or societies you belong to and can make friends from completely outside the university as well, if you want to. In terms of social background, while you'll inevitably meet people who have been to independent schools, anyone who thinks they're in any way 'better' because of it isn't worth the time of day. Most students will end up having a mixture of friends who come from different backgrounds and don't judge people on the kind of school they went to.
Next up, getting a 2.i or 2.ii is NOT embarrassing. Studying at top universities is hard. Coming out with a degree of any description is a massive achievement. I have never met a Cambridge student who takes academic competition between colleges seriously. Anybody who thinks below a 1st is embarrassing (which is not the majority of people) is probably not someone worth spending time with.
Finally, you're absolutely not obliged to feel grateful for being made an offer. Your emotions are your own, and they are valid. When making the decision of which institutions to firm and insure, think about the course and where you think you'll be happy. You have plenty of time to make that decision yet, so make sure you do your research thoroughly so you're able to make an informed decision. You wouldn't be letting anyone down by turning down your offer, just as you wouldn't if you turned down an offer from any other uni.
On that note, I'd recommend contacting your College's Admissions Office or JCR (student committee) who will be able to talk you through your worries. Many colleges will have offer holder events, either online or in person, where you can meet some current students and other offer holders. The same will likely be true of other universities as well - do go along to offer holder events for universities you're seriously considering firming or insuring as well, if you can.
I hope you find this helpful