Do any philosophers take Modal realism seriously? How? Why?

In Short “No”.

We can in mathematics assert axioms and fail to or choose not to assert axioms.

In logic, we can assert axioms and fail to or choose not to assert axioms.

In reality (the existential universe) we discover laws, or fail to discover laws – we cannot assert them or fail to assert them.

We can therefore assert in logic, mathematics, a contract or legislation, a work of fiction, of fantasy, or of theology, that which cannot be exist given the laws of the universe.

We can testify honestly without due diligence, other than to limit our introduction of imaginary content we did not observe exists. We cannot testify truthfully to that which we have not performed due diligence against the existential possibility thereof.

So we don’t take theology, fantasy, fiction, nor axiomatic logic and mathematics into evidence in court because one cannot testify to them.

We only take theology, fantasy, fiction ‘seriously’ as entertainment. And axiomatic logic and mathematics to be taken seriously only as entertainment. Much like we find Numerology, Astrology, and justificationary Philosophy as entertainment (puzzles) before we move to the detective story, slow reveal fiction, and slow reveal fantasy. These are entertaining puzzles, and nothing more.

We take ‘seriously’ that which costs. What separates Law, Economics, the Sciences, Physics, mathematical physics, from pure mathematics, logic, fiction (which does abide by a logic), and theology (which does abide most of the time by some set of justifications), is the cost of doing versus imagining.

While we cannot in fact LOGICALLY know which scientific theory to prosecute, we can know which is least COSTLY to prosecute given the anticipated returns. And it turns out that in fact, for this very reason, decidability does exist in the pursuit of scientific theory: Cost.