I've ready this with interest as one side of the family is very WC and the other very MC but over time the incomes/money have evened out, even to the point where many of the WC side have far more money, and yet the WC families still have far less opportunity.
My honest opinion is it starts being money and that creates an outlook/culture/thoughts towards opportunity that means WC people on the whole, even when money isn't as big a factor as it used to be, don't have the time or mental reserves in the same way to do new things, nor do they have the confidence as it is more likely to be out of their comfort zone. If you consistently don't do new things and don't go out a lot to new places, it can seem bigger/more anxiety provoking. This takes place in many forms - bright children going to local comp despite teachers making it clear they could get into the top selective schools, enough money for new holidays and far flung places yet going to the same type, or even place, each year. And then smaller things like weekends being for cleaning, food shop and watching programmes, despite there being the time or funds to do more.
I do think initially it comes down to money (lack of) but that creates norms and a culture that remain for many even when money situations change. I see this so much in my job, within my friends and family and even to myself to some extent. I grew up MC and have a MC education, but due to life circumstances am much more WC in terms of income and options for a variety of personal reasons and as a result I can see even with just one decade of identifying more with WC friends, that I've changed. An afternoon out now feels huge, I'm more likely to want to cancel it, I am very task and home oriented now, I think differently to how I did a decade ago. It's hard to explain but the only friends whose weekends I identify with now are my WC friends. My MC friends who are out doing lovely things, often even free things, I can't relate to at all. I no longer have the confidence or time resources - there is no option of any paid help. And it just feels huge to give up a day when I could get tasks done, for leisure. Remember years ago (for centuries) leisure was only for MC and UC. It was not an option for those in the working class culture.
Take older relatives, the ones on WC side will tell me this week they've done the food shop, gone to Dr's, and what they've cleaned, and what family they've seen. A rare week there will be a treat, usually something someone else arranged. MC older relatives who have no more money will talk about which NT property they visited, lovely walks they've taken, coffee shops they've been to with friends, new cities they went to or re-visited on a day out. Why? They are culturally brought up to have leisure and have the confidence to do different things without the anxiety of feeling they need to focus on tasks.
Interestingly my line manager and I were speaking about this yesterday. Her weekends are full of fun and they do things I can't imagine having time for. This past week they made something like 50 cakes for a charity event, all went trampolining, went to a gorgeous stately home for lunch etc. We have the same number of dc (3), hers are involved in very serious sport (national teams, could be headed to Olympics down the road) and I asked how on earth they manage it all, that my weekends involve each of the 3 dc doing one activity (and even that is super stressful for me and takes me away from tasks), food shop and cleaning. She is one of those people who checks her privilege and admits it (rare imho) and she said "Ruby, you have to understand how different our lives are because I have money. I have a cleaner every M/W/F who does everything - laundry, changing bedding, vacuuming, sweeping, ironing, washing floors, even picking up the dog poo in the back yard and running errands. Some weeks she even does the shop. I don't have to think of anything to do with the house it's all done. Monday she would even wash all the cake pans if I couldn't bare it, but I made myself and dh do it as it didn't feel right. If something goes wrong we bring in help immediately or just replace it, we have two tumble dryers and if one is slow or not working properly out it goes. We have so much more free time because we can pay. And when kids were little we always had an au pair, it's why I was able to get to the gym within weeks of giving birth. When people would comment on how good I looked, it really was a reflection on the money we had to make me look good".
The other area you really see this (and I was a lecturer for many years prior to this past decade of things being harder) is University choices. On the whole and there are many exceptions, when WC kids get to Uni they stay close to home, even if there are the funds, it is their parents who are more often dubious about the whole thing. The middle class and upper class kids are far more likely to go far from home. I lectured at a good Uni and some of our brightest students were from working class backgrounds, by far. They never thought to apply to top Uni's, were never encouraged to, and when we discuss where they could go for masters they were adamant they couldn't go to the top 10 and were perfectly fine at the local one. Many of my MC kids didn't have the grades to get into top Uni's but felt they would. It always was a point of interest for us as lecturers and registrars.