If they can move quickly and avoid eviction/unlawful detainer on their legal record, it will be better for both of you. 

It is unlawful to "discriminate in any aspect of selling or renting housing or to deny a dwelling to a buyer or renter because of the disability of that individual, an individual associated with the buyer or renter, or an individual who intends to live in the residence."

If the property is in SoCal, the process is as follows:Serve a 3-day notice, and assuming they do not pay, you file an unlawful detainer. 

Can anyone think of reasons that this is a bad idea or may be unlawful in some jurisdictions?

Since these folks are not tenants, but the seller who has not vacated the premises, you really have an unlawful detainer on you hands and an eviction may not be the appropriate remedy.  

This to be an incentive to leave the place clean and undamaged.And explain that if you file an unlawful detainer (or whatever the eviction proceeding is where you are), that will go on a database that will show on eviction reports that future landlords will pull - even if they win the eviction proceeding. 

And I'm not a lawyer and don't live in CA but:http://law.onecle.com/california/penal/25605.htmlhttp://law.onecle.com/california/penal/26035.html"FIrearmS In tHe Home, buSIneSS or at tHe CamPSIte Unless otherwise unlawful, any person over the age of 18 who is not prohibited from possessing firearms may have a loaded or unloaded firearm at his or her place of residence, temporary residence, campsite or on private property owned or lawfully possessed by the person .

Our local rental association keeps a list of Unlawful Detainers that were filed, but it is printed on a month-to-month basis.

THE BOARD'S FINDING THAT APPELLANT ENGAGED IN UNLAWFUL HOUSING DISCRIMINATION IS CLEARLY AGAINST THE WEIGHT OF EVIDENCE.

. "** "...in addition to any other action which it may take under this section, award the petitioner damages, which damages shall include, but shall not be limited to, the expense incurred by the petitioner for obtaining alternative housing or space, for storage of goods and effects, for moving and for other costs actually incurred by him as a result of such unlawful practice or violation."*** "ad•judge(əˈdʒʌdʒ) v.t.