No animals or smokers.

I would include a question: "Are any applicants indoor smokers?"

We have had to remove one trailer full of trash including everything from TVs to smokers to pallets.

Our prelim scoring is based on objective non-discriminatory items, such as if they are smokers, if they have lived in the area (have roots), have held job for over a year, income, how long they have stayed at previous addresses, how long they intend to stay, Facebook/google search, unverified look at criminal, bankruptcy, evictions, bank accounts.  

I think renting to a former manager is kind of like dealing with a former smoker.  

Smokers please do not apply.WHAT IS WRONG WITH THIS AD?

So we accepted this person ( single person, good income, good credit, no pets and non smoker). even though the move-in date is 5/1st.

I don't know what California's laws are, but I would think you are safe to do as you please, its no different than not allowing smokers. 

Smokers, lawyers... 

If you see them smoking in their car before they come to meet you, you can deny them because they are smokers (if that's in your criteria).So, have tough criteria, and apply it evenly to everyone, and you will not likely have to ever rent to a Section 8 tenant.