If they have anti-social disorder, especially if they have committed sex-offences no one wants them, and they might have other felonies as well.The non-crazy SSDI recipients fare better; they can get along with a room-mate and since they are more sympathetic, they'll probably have better luck finding subsidized housing. 

Some jurisdictions forbid minor children from sharing a room with those of opposite sex.

What if you seller is the opposite sex?

What the hell does that mean you sex monkey you?"

But in our marketing campaign we're taking the family business angle and giving potential clients the ability to deal with either myself or my wife, I'm hoping the option will appeal to both sexes.

There's nothing wrong, illegal, or immoral about screening the tenant by phone.Explain your basic standards, particularly anything that would automatically disqualify them like a pending bankruptcy, sex offenders, or lack of a Landlord reference.

I know you can't discriminate against race, religion, sex, handicap, LGBT, emotional support and service animals, now they are adding co-signers, lol. 

I'm not sure what a "full disclosure landlord" is, but I would not use that term as tenants may take it as you've done all the research for them regarding crime, sex offender list, potential school district changes, etc., which I would not hold myself responsible for unless your state requires those disclosures from the landlord. 

For all you know the husband could be a registered sex offended and that's why he's not on the lease and the rent is paid by someone else There would have to be something substantial for me to not renew them, but I want to know who I'm dealing with now and not after the fact when its too late.

The reason why is that in some states, there are limits on how much deposit you can legally charge before it is perceived as a downpayment for a land contract or contract for deed.If they have a good job (and I am assuming you got 3 months of paystubs and called their employer to prove employment) and a $7500 deposit, and no criminal record (theft or fraud or violent felony or sex offender), then by all means accept them as tenants.