Spork Well said
It's important to know that class affects people. You can't even begin to tackle social mobility issues etc until you understand the basics of class and how it influences people
Do I obsess about class? No. I know where I fit in and where my children fit in. I don't talk about class a lot, certainly not with my friends irl.
I do think that in recent decades the way we decide who is in a certain class has changed a bit. I was born in 1965. When I was a kid in the 70's, class was much more about family background than it is now (your background still plays a part now but other factors have increased weight when we decide what class we and others are in). There was still a more Victorian way of looking at it than there is now
And to some extent, we still have a Victorian viewpoint. Mostly when it comes to the 'upper class'. Being Upper Class, in most people's minds, is heavily dependent on your family background. Upper Class usually implies inherited wealth, land ownership and titles. A Duke is upper class. Even if he is having to sell off half of his possessions because he's massively in debt.
Society has changed in the last few decades, and with it our views on class have changed a bit, and suddenly we are thinking about education, income, and habits more and more
Either way, if you think class doesn't affect you, then you probably largely mix with people in the same class as you. In my mind, not noticing class is a bit like not noticing white privelage, the way the security man at the shop is only following the black male teenager around etc etc. "oh but it doesn't affect me". Well it does. But not as obviously as it affects that teenager. It does affect you, but you arent conscious of what you have (or don't have).