Dittany, I'm relatively new here and I have no idea which members describe themselves radical feminist, liberal feminist, conservative feminist, separatist feminist or any other term. I only go by what people say so didn't realise it was specifically radical feminists here who were challenging the use of the term Kyriarchy.
As you say, radical feminist views may occupy a "very marginal form of feminism when you're looking at the whole picture (of feminism.)" But, they can still benefit from social, economic and political privilege by virtue of their ethnicity, being non-disabled, class background, cultural heritage and education. Holding radical political views doesn't erase all these privileges, even when they actively seek not to engage with them.
So, my unease still rests with the idea that feminists who hold other non-gender based privileges rejecting the use of self-identification terms chosen by other feminists who are marginalised due to their "less favoured" ethnicity, class, culture, education, etc.
Cats, you also have a point about the slightly differing origins of feminism in the US and the UK. In the US, for example, there were strong connections between more liberal Christian groups (e.g. Unitarians, Quakers), the Temperance Movement and feminism/suffragette movement. Some, particularly Lucretia Coffin Mott (who was a driver of the abolitionist and feminist movements) and Carrie Chapman Catt (founder of the League of Women Voters, but also an avid campaigner against anti-semitism) were better at recognising the interconnectedness of oppression. Sadly, Elizabeth Cady Stanton espoused some quite abhorrently racist and classist views.