How is extra exam time for disability accommodation perceived by professors, especially potential reference letter writers?

(I will answer in the context of the U.S., but I hope others will answer for other parts of the world.)

How is this perceived by professors? Might some of them think that these students get an edge or advantage over other students unfairly?

The US Department of Education's Office for Civil Rights (OCR) has stated, "A test should ultimately measure a student's achievements and not the extent of the disability" (www2.ed.gov/about/offices/list/ocr/docs/auxaids.html).

If some professors are still playing catch-up, that's their problem. Extended time has been settled legally for at least 15 years (see the Marilyn Bartlett case about accommodations in the bar exam, which was decided TWICE by Sonia Sotomayor, long before she was appointed to the US Supreme Court).

If a student is looking forward to requesting a reference for grad school from a certain professor, would it generally be better for him/her not to request exam extensions for this professor's course?

There is no reason to have a tooth extracted without novocaine, i.e. there is no reason to sacrifice the needed accommodations, just because a professor might botch a letter of recommendation. I say botch because it would be discriminatory for a professor to judge a student's exam results differently just because the student used a reasonable accommodation to achieve them. OCR enforces the Americans with Disabilities Act (ADA) and the Rehabilitation Act, which protect the civil rights of K-12, undergraduate and graduate students with disabilities.

Institutions of higher learning and testing boards do not provide extended time and other accommodations lightly. It is fair to assume that if the student has an approved 504 accommodation in place, it is in fact needed and appropriate. College professors are experts in their fields. We cannot expect them to also be experts in disabilities, and sit in judgment to decide which students truly deserve their legally binding accommodations and which do not. It would be even more absurd for them to make such judgments without a careful examination of the student's documentation. And if we did hand off this responsibility to individual professors... why would universities need to set up offices for students with disabilities?

I think, as educators, it is not our place to judge whether this extra time granted to students according to disability services is an "unfair advantage" or not. I am a mathematician, not a psychologist, so it's not my place to diagnose them or argue with someone else's diagnosis.

There is obviously considerable research done by people who focus on these types of issues that suggests that these are reasonable accommodations for these students, and I think that should be respected.

Timed exams are usually a function of larger, lower level lecture courses. As such, I don't really keep track of who has a letter or not.

The best grad school letters come from professors who've you've worked with individually, in seminar or lab. Evaluations in those cases are individual and less reliant on disability accommodation.

Tl;dr: ask for the accommodations you need to excel in the lecture courses. Try to take small seminars, work in labs, or do a junior or senior research project with a professor if you want a strong letter of recommendation that will help in grad school admissions.