A person's career choice does tell you something about them, but it's far from the most important thing. I don't think it's valuable as a sole indicator of what sort of person they are or how well you'd get along with them.

As to social status: if someone is willing to befriend another when they have one sort of job but wouldn't be willing to befriend the same person if they had a different sort of job, I think that someone is cheating themselves.

No, it's not the most important thing (far from it, as you say). But it's a thing most people have, and a thing that most people are willing to talk about, and a thing that is socially acceptable to ask about, so it's a decent first question. It also has the virtue of not being too intense or intrusive.

Other first questions could be "What is the core of your identity?" (though that might be too intense/intrusive) or "Of all the things we could talk about, what would you be most interested in?"