Michelle Malkin was not prohibited from using AirBNB because she was conservative. She was banned because she associates with American Renaissance. American Renaissance is not a conservative organization. They are (to be generous) a race centric organization that focuses on "defending"/promoting whiteness. While there may be some overlap between their beliefs and some positions that are considered republican or conservative, that is in no way the focus of this organization.
There is nothing conservative about a focus on skin color, regardless of what that skin color is. Reducing the size and scope of the federal government promoting the rights and liberty of the individual over the collective (all individuals, regardless of the skin color of the individual) are conservative starting points. American Renaissance is only vaguely interested in things of this nature; their focus is on race. Focusing on race (regardless of the race in question) is repugnant.
Are they racist? Probably, at least to some degree. They're not the Klan, but I would think that they would find more common ground with them than they would differences. Basically they perform a similar function to what Sinn Fein did for the IRA: try to defend the indefensible.
That said, they are no more (or less) racist than BLM. Assuming that AirBNB is not shutting down the accounts of people affiliated with BLM, Malkin has a legitimate complaint.
But she was not booted for being a conservative.
“Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy. It's inherent virtue is the equal sharing of miseries." - Winston Churchill