Will getting rejected from a graduate school affect my relationships with the faculty members at that school? I recently got rejected from quite a few grad schools.  Will this make it harder for the faculty at these schools to take me seriously if I interact with them?

In particular, I'm interested in having a particular professor at the school I will be attending as my advisor.  However, until a few month ago, he was a professor at a school I got rejected from.  I'm afraid that he will refuse to work with me, knowing that I wasn't qualified for the graduate program he was recently at.
I got hired as a postdoc at a university which had rejected my graduate application.

And not just that. When I started, I realized that they had made the right decision. The background level of the first-years was uniformly and substantially higher than what mine had been when I started. I would have gotten creamed.

You will have the opportunity to prove yourself in your first year. Do a good job, and any weaknesses in your application will be quickly forgotten.

Good luck!