Many of the most important issues for LGBTQIA+ people are going to be found in local newspapers, newspapers/journals for the LGBTQIA+ communities, and in endorsements for or against things like marriage-equality, trans rights, book bans.
1. Use the resources here to investigate your candidates: https://subjectguides.library.american.edu/downballot
2. Endorsements:
3. Records of behavior against LGBTQIA+ Rights
4. LGBTQIA+ News Sources