Is it rude to ask for accommodations due to a learning disability? I have a learning disability where I can only learn through seeing (not seeing and hearing). As a result, I need to have headphones in class to block all sound. Should I just tell the professor this?
It would not consider the request rude, as long as you have a reasonable justification for needing to wear headphones during class (which you do). How you might approach your professor and whether he'll accommodate your request may depend on where you're located and whether your jurisdiction provides protections for individuals with disabilities.

In the United States, for example, individuals with disabilities are protected though the Americans with Disabilities Act (ADA), which require colleges and universities (amongst other organizations) to provide reasonable accommodations for individuals with disabilities—in your case, needing to wear headphones in class would be considered a reasonable accommodation (although this might depend on the subject of the course—in a woodworking course where headphones would pose a threat to safety, for example, it would likely not be a reasonable accommodation).

There are also proper channels a student needs to go through to request medical accommodations—initial requests should not go directly to the professor. Universities and colleges will have a centralized student disabilities office that handles requests for disability accommodations and it is this office that will require documentation of a disability and determine what accommodations a professor will be required to provide. They will then send a form to your professors indicating what accommodations they need to give you. Because of ADA and health privacy laws, the disability office will not tell your professor what your disability is and your professor is not allowed to ask you what your disability is. 

Although this answer is very much local to the United States, similar protections may exist in other countries as well. Rather than approaching your professors directly, consider asking your university's student advising office, student life office or health clinic whether professors will provide accommodations for disability (you shouldn't need to tell them what your disability is). They will then be able to point you to resources that will work with you to find solutions.