Can a paper be rejected because another paper (by someone else) based on its arXiv preprint extends the result? Suppose that I put a paper to Arxiv and submit to a journal at the same time. Someone extends my result and clearly cites my paper. This is totally fine. They submit it to a journal. For whatever reason in the review process, their paper is published before mine is accepted. Do I now have to worry that the referee will reject my paper on the grounds that a better result exists, even though they acknowledge that they get the idea from my result?
On the one hand, referees can reject your paper for all sorts of foolish reasons. I would not if I were refereeing, but that means nothing for some random person with an axe to grind.
I wouldn't worry about this scenario too much though, because it would require some relatively extreme timing to happen.

On the other hand, even if it did happen, if people are citing you and you are having an impact, is it really that much of a problem if the paper is "just" in arXiv? Only the most blind and foolish Impact Factor junkies would hold the lack of brand name against you. Also, you will write many papers in your career, and I would be startled if such a situation happened more than once.