How important are physics and other non-math courses for admission into a math PhD?
Math grad programs do not look at physics courses on the transcript, or think in those terms. 

The point is that higher-level (not formulaic) physics courses can be beneficial to math people by providing other inputs for intuition. A common obstacle is that the higher-level physics courses do speak in terms of the lower-level ones, which are often quite alien to/from any sensible mathematical world-view.

But if one skips over those "immediate" things, one can find that there are "physcial imperatives" mandating mathematical "facts"... which might not be obvious on "purely mathematical" grounds.

The grandest example is "Green's functions" ... about which volumes can be written... An immediate point is that the idea is wonderful, is necessary, even if one cannot justify it. Green got the idea pre-1850, and it was completely understood in "rigorous" terms by L. Schwartz in 1950. Not easy, ...

That is, understanding other (very serious) inputs to mathematics is obviously helpful.