You can deny housing to sex offenders on the Registry, and not violate the Fair Housing laws, as long as you turn down ALL sex offenders on the Registry. If you are using the Registry as an excuse to turn down somebody who is Hispanic, for example, but White offenders are allowed housing, then you will be in trouble. My authority for this statement comes from the United States Department of Justice information page regarding Fair Housing Act at https://www.justice.gov/crt/fair-housing-act-1
You can also deny housing to anyone who has a criminal conviction for manufacture or distribution of illegal drugs, no matter when the conviction occurred. Same thing as the sex offenders–it can’t be an excuse to turn down some people and rent to others with the same history. My authority for this statement comes from 42 U.S.C. §3607(b)(4); See, also Office of General Counsel Guidance on Application of Fair Housing Act Standards to the Use of Criminal Records by Providers of Housing and Real Estate-Related Activities, April 4, 2016, at pg 8.
Aside from that, you are not allowed to have a blanket prohibition against people with convictions within a certain time frame. HUD says you must take into account the type of crime, the age of the person at the time it was committed, how much time has passed, and rehabilitation evidence in the meantime. Wish I could be less vague, but HUD hasn’t provided any more guidance than that. My advice-continue to turn down people convicted of violent crimes or arson, or multiple property crimes such as theft, and don’t worry about drug use offenses more than a year old.