Unfortunately, many of the most vociferous of those who describe themselves as "feminists" seem to fall into the second category.
Feminism has become too broad a church for it to be possible simply to categorise oneself in terms of whether one believes in, or supports, "it". The same is true of equally vague concepts such as "liberalism" or "socialism".
There is a mild version of feminism, which goes something like this:
"Many women are more capable, and more keen, than the majority of men. Their gender should not act as a handicap to their career progression."
Most people would probably give their assent to this — which is not to say disagreement with it should be taboo.
There is also a strong version of feminism, which says:
"There are no statistical differences between men and women, at least none that ought to matter. Therefore any difference in average outcome reflects injustice, and society should do something about it."
Fewer people would endorse this version.
These are just two out of the many different positions that have been described as feminism.
But some feminists seem not to want such distinctions to be made. A person who indicates they may support the mild, but not the strong version, is liable to be accused of being anti-feminist (and possibly misogynist).
So e.g. Dominic Raab voicing a mixed attitude to the concept of feminism generates reactions like the following, from Harriet Hall in the Independent:
We have to acknowledge that rape is a misogynist crime; that the gender pay gap and all the complications surrounding it are a result of sexism; and that the bloody, inhumane act of FGM is purely to control women. The only people who benefit from a reluctance to utter the name of the one movement that seeks to protect women, are the men who oppose it.Hall goes on to condemn Raab's opposition to positive discrimination, and asserts that feminism "can't be sugar-coated to soften the message and appease the patriarchy". She concludes: "Sorry, Dominic Raab, you have only two choices: you’re either a feminist or a sexist – there is no in between."
Whom does the refusal to explore in detail the meaning of "feminism" serve? Presumably, those who want to pursue a programme based on the strong version.
It has become disreputable to sound negative about feminism in any way. This can be more easily exploited by extreme feminists if there is no identification of different levels of feminism.
A resistance to allowing counterarguments to be aired is comprehensible — though not admirable — if people fear this would undermine a programme they believe is morally correct. Unfortunately, many important topics nowadays seem to be treated in this fashion, allowing politics to override data or analysis.
It's a question of priorities. Are you predominantly concerned that people should be able to think about a topic, or predominantly wanting people to come up with the answer you 'know' to be correct?