Just gender, race, sex, etc.

These laws prohibit discrimination based on race, color, national origin, religion, sex, familial status, disability, and other protected characteristics.2.

-Can property values decline due to registered sex offender living in area?

You run the criminal background check to confirm if a applicant is a sex offender.Bottom line is you still have the ability to reject any applicant you choose for personal reasons even if it is their appearance, attitude smell etc.

My second thought was how much I would hate to be across from a school if I were renting it - the noise level and the periods of high traffic in the area would be downsides I'd be sure to mention in a review.My advice would be: if you want to move forward with it, look into the local laws re: convicted sex offenders to make sure you can conform to them, and prominently disclose in your listing that you're across from a school.  

I've heard about signs like these and they are possibly sex trafficking rings.

Which includes: criminal, credit, prior eviction (wouldn't help now with Covid,) plus checking their sex offender status and social media.You would think that those screenings are enough, I know I did.

I do care about:Work history - I call the employer to verify income and tenure of employmentincome 3x rent.evictionscriminal - big offenses - sex offender, robbery, etc.  

Violent crimes, assault and sex crimes are certainly a serious matter.There was a case where a woman fired a gun at her abusive husband as a warning that wasn't even close but in his general direction.

@Bao Huynh Congratulations!