You cannot deny them based on a multitude of things, such as familial status or sexual orientation, but you can absolutely deny them based on them having a prior eviction, being smokers, not meeting your criteria like too-low credit score. 

In secure markets we offer cutting-edge Self-Showings for prospect instant gratification – which leads to more showings and less vacancy time.

You have to make smart choices, put in the effort, delay gratification, and sometimes even sacrifice.

Whereas you owner occupy a fixer in the same neighborhood with great school district, you definitely defer gratification for a little while.  

Sacrifice is delayed gratification and often doing things that make you uncomfortable.

Say physical/sexual abuse.

Delayed gratification requires some sacrifice.

No one would ask on an application form what the applicant's sexual orientation, religion, race is etc...so why would you ask about ESA? 

Most everything else is instant gratification.

As other comments have mentioned, having weak financial skills may not translate well into real estate success as success in real estate has a lot to do with delayed gratification.