Should you publish a rejected conference paper on arXiv? Imagine you have a paper that got rejected from a top tier conference. You think it is of high quality.

Do you submit the paper to arXiv, or keep pushing for a conference later on?
Submitting a paper to the arXiv does not preclude publishing it later in a journal or in the proceedings of a conference.  In fact, one should not think of a paper which appears on the arXiv as being published. (There's no peer review, for one thing.)

In my community (hep-th, mostly) one always submits to the arXiv first, gathers comments, and only then submits for publication.  Of course, other communities might work differently.

In the fields I am familiar with (maths and physics, mostly), I would submit the paper to the arXiv in any case.  You can then decide how to actually publish the paper.