Florida Senator Blaise Ingoglia (R-Spring Hill) has introduced SB 1248. It would cancel the party recognition of any political party that had ever supported slavery. If it were enacted, the Democratic Party could get back on the ballot only by choosing a new name. Also it would lose all its registrants and need to start from zero. See this story. Thanks to Eric Wong for the link.
Ironically, in 2019 a Democratic State Senator introduced a bill in California, SB 696, that would have removed the American Independent Party from the ballot unless it changed its name. It passed the legislature, but Governor Gavin Newsom vetoed it.