I find it unlikely that one person could provide in-depth sensitivity advice for everything. A person needs to be very well-versed in an ethnicity, culture, religion, disability, gender, nationality, mental disorder, etc. to be able to provide useful feedback. Ideally, it would be someone actually from that background. There's no course that's going to teach someone how to be an expert at all these things.
I think "don't be a dick" covers most sensitivity issues. If you don't have personal experience in what you're writing and it's a potentially sensitive issue, and you can't find an expert to interview, don't write it.
That probably covers 90% of sensitivity issues. For the other 10% there are writers' boards, forums, and social media to ask questions of people who have in-depth, personal knowledge.