@ScottishAngryBird in the UK, it is an identity... As I said upthread, my DH has a colleague who is a VP in an investment bank, he earns well enough to buy a 4 bedroom house in the home counties on a single income which is no mean feat these days. Yet he calls himself working class (despite having a university degree and a well paid job by most standards). There are many many people who identify as middle class who are poorer than him.
In America, it's more tied up with income. Of course in America, cost of living and salaries can vary widely but generally a middle class family owns their own home, has good health insurance, a college fund for their kids, pensions, money for holidays, savings and is able to afford consumer goods like the latest technology. Basically enough to live off and enjoy holidays and also some to save for old age as well as education/future healthcare needs. Which is why when they say the middle class is shrinking, they generally mean the economic middle class- it's getting harder to buy a home, pay for childcare/university education outright, save for retirement on an average salary plus also enjoy life a little. Ability to shop at waitrose or a higher priced shop because you like it/it is more convenient than always defaulting to the lowest priced option.
Also nowadays due to the high cost of property in metropolitan areas, many young people are either priced out of home ownership or aren't interested in it (more interested in other alternative investments like crypto). But they generally still can afford property, just in less fashionable locations and often they also have expensive tastes//hobbies i.e. soul cycle classes; lots of expensive restaurants and bars. Like many of the renter's in my block probably don't have low incomes and they probably earn more than us given that their rent is higher than our mortgage but they still are able to afford BMWs, pedigree French bulldogs and Gousto boxes for every meal. I wouldn't consider them to have a typical working class income in the American sense. Of course in the British sense, you can earn 300k and still call yourself working class if you grew up on a council estate in Nottingham and prefer football to the opera and shop at ASDA. So yes I guess your sister can be MC because she identifies with it and she probably has a reason to.