"Do philosophers seriously analyse themselves in order to understand why they believe the things they do? Or do they, like so many other people, accept uncritically any thoughts which appear in their conscious minds."

You ask very good questions. I would say that an average run-off-the-mill absolvent of philosophy does not spend much time (if any) analyzing themselves. I guess, the same can be said about scientists. On the other hand, I'm fairly certain that people like Chalmers, Kastrup, Goff, but also e.g. Dennett spent a lot of time observing the workings of their minds, exactly "in order to understand why they believe the things they do." Well, but to be honest the motivation was probably more general (i.e. to understand why people believe what they do) — best to ask the folks themselves.

Anyway, this phenomenon (lack of self-knowledge) is not unheard of in the circles who's sole purpose is to deal with self-knowledge. So, that’s that.