He was also convicted of some kind of sex crime 11 years ago as well so the house would be listed in the register if he lived there.

Avoid anyone with sex charges or with anything violent in their criminal records....no matter how long ago they assaulted someone or with drug charges. 

If the guy is a registered sex offender, go to the police ASAP and ask if he's registered for your address.

I'm not a lawyer, but I'm almost certain that there NEEDS to be a reason in order to be discriminated against, such as race, religion, sex, etc.Unfortunately for you there is no law that says what type of flooring a unit needs to have.

Is there a niche for renting  C and D class properties to sex offenders?  

If they refuse, evict them and get them out.You may also considering screening all your current occupants to clean out any drug dealers, sex offenders, etc.

A charity case best I can tell, registered violent sex offender against children, at $300 a month including utilities. 

Encourage all that want to apply to visit the Megan's Law website where they can view  information on the registered sex offenders in the area.

Does anyone search the sex offender registry to see if there are any close by before they pursue a property?

Violent criminals, drug users, drug dealers, prostitutes, sex offenders, and many other criminals run a very high risk of offending again and I wouldn't want to expose my other tenants to that.