Such an interesting thread!
I wanted to add to the discussion of intersectional feminism and radical feminism that they don't have to be mutually exclusive, though they can be treated that way, too.
Radical feminism is based on the idea of going to the 'roots' of women's oppression, and those roots are seen in sex: The desire by others (mostly men, but also wider groups such as families which are led by men) to control female bodies in order to control reproduction and the access to those bodies for heterosexual intercourse which men desire. The means used for achieving and maintaining this control include gendered roles, norms and stereotypes which have traditionally been based on laws, religious beliefs etc.
Intersectional feminism, is in its earliest (and, in my opinion, the most correct) form is about the importance of analysing how sexism and misogyny affect women differently based on how other forms of oppression also affect them.
It's the intersectional aspect between two or more forms of oppression which can affect how different women experience sexism and misogyny and how it might affect their lives differently. Class, race, ethnicity, sexual orientation and age are some of other types of possible oppression bases which need to be considered in the same context as sex-based oppression.
These two approaches are quite compatible, in my view.
This is not so much the case in some more recent interpretations of intersectionality which dispense with the sex-based oppression axis altogether. Once you do that, your feminism cannot be radical feminism.
In fact, I think it has stopped being feminism altogether, though those who prioritise gender identity over sex disagree.