I'd argue that TERF-ism, especially JKR's brand of it, has both classist and racist elements ingrained within it

The whole ideology is based around gatekeeping 'womanhood' to a single shared demographic experience, denying feminism to those outside of it

There are ways in which trans women have had differing experiences of femininity from cis women. But the same is true of black women of white women, etc

It might be explicitly anti-trans; but it's implicitly anti-in-group