I think DMcG is right; she's hardly the brightest bunny in the hutch, and seems to have latched on to the views of an odious group rather through ignorance than anything else. Were she to be sacked, I'm sure that odious group would immediately claim her as a martyr, and its fellow travellers among the readers of the Daily Mail and the Daily Express would weep and wail about "political correctness gone mad" and sundry piffle. So let's not go there, as they say.
If she were a schoolteacher or anyone else charged with the care of others, then maybe one would find her views incompatible with her job, but she is after all, just a hoofer.