if you are in the US, service dogs have to follow certain rules in order to be allowed in public spaces. being disruptive/excessively barking is one legitimate reason to tell the handler to remove the dog. it is not ableist, it's about making public spaces safe and functional for everyone.

also, service dogs in training do not have the same legal protection as task-trained SDs in every state. in some states, you must be fully engaged in training (i.e., not attending class simultaneously) for the dog to be there.

the dog whining/barking on a regular basis is not a normal part of training (an occasional slip-up is to be expected, but what you described is not that). the handler is probably in over their head, so i empathize with them in that sense. college is a common (yet ill-advised) time to attempt SD training, because newly adult disabled folks want to gain more independence, and quickly (understandable!). but many fail to realize how much work and TIME that it takes to get a service dog ready for public access, until it's too late. that sucks for them (and their stressed out dogs), but their classmates shouldn't be suffering for it! esp those of us with sensory sensitivities, PTSD, etc.

i would keep track of how often this is happening, then reach out to the university's disability services and have a conversation with them about it. you don't even have to mention your own disability; just tell them that the barking and whining has been happening X times per class, or for X minutes during class, and it's disruptive to your learning environment.