Lived in or near Cheltenham all my life. Of course, you'll certainly find your tribe. There are lots of different people here. Other than the odd special occasion, I live in jeans, tracksuit bottoms, leggins and mostly wear trainers. I don't wear makeup and have my hair cut twice a year. Despite this, I'm very lucky to have eight life long friends (at least I hope they are, the least I've known one is 15 years). Two came here from other countries, six went to uni (I didn't). One goes to two local choirs, another to one of those. I have a doggie friend, used to walk with her a lot but not so easy with working hours. She takes her dogs to two dog training/obstacle type classes and so many local people go out late afternoon, she ends up meeting her 'doggie' friends in the park - you have to laugh there's usually a group of 4-10 people talking while throwing the ball for their dogs. If I go out walking with her up the hill, I often see others with friends.
I totally disagree Cheltenham isn't friendly. I have a high contact job and also come across quite a few people who I pass the time of day with outside work. Others have mentioned, I'd say 15% children at our local school do not identify as white. Not sure what percentage are part of the LBGT community, but workplaces do try and address this and I'm certainly not aware of any problems in my two jobs.
I would say, if budget/accommodation permit, I would choose Cheltenham over Gloucester every time. There's a lot more to offer in the immediate Cheltenham area (and of course you're surrounded by hills) and also it feels a lot safer. If you look at Gloucester, do take your time to walk around the city centre at different times of the day (maybe not too late though, I'd feel a lot safer in Cheltenham late at night).
Like everywhere Cheltenham does have it's less than ideal areas. If you have to consider social housing or nearby, I'd avoid Whaddon/Princess Way and roads just off and Manser Street and surrounding streets in St Pauls, they're a big no.
Not sure how often you'd be getting the train, but the D bus is one of the more regularly routes and operates late at night (some don't), so you might want to consider other areas on that route, Hatherley, near Pittville Park and there's a lot going on in Bishops Cleeve for all ages.