Should I write that a student is a feminist in my recommendation letter?

First of all, your title doesn't quite match the rest of your question. In your suggested quote you write "she is very interested in advancing women and other minorities in the STEM field," whereas according to the title you are asking whether you should write "She is a feminist." Sadly, these things will not evoke equivalent responses in all parties -- the word "feminist" has unpleasant connotations in certain circles nowadays, more so than a generation ago. (By the way, I am a feminist, and it makes me sick that the word is now taken in this way. But it is by many, and so I think it is too loaded a word to use about someone else in such a context.)

The purpose of a recommendation letter is to successfully convey your impression of the recommended party. In particular, if you feel strongly that the recommended party should get the position being applied for, then you want to write the letter that maximizes the chance of that happening (while staying appropriate, professional and truthful, of course). With that in mind: how relevant "she is very interested in advancing women and other minorities in the STEM field" to the honors program the student is applying to? Is this advancement one of the activities that students in the program will be participating in? Or, beyond interest, does the candidate have a record of activities and/or accomplishments in advancing women and other minorities in the STEM field? If the answer to either question is yes, I would suggest that you fill in further details accordingly: this is part of your argument that she is great fit for the program. If not, then: are students selected for the honors program because of their progressive views -- or, much more cynically put, because of the alignment of their political and social views with those of the administrators of the program? Probably not, right? In particular, because "She is fantastic and I assume that she will get admitted," then I don't think you need to help her out in this particular way. There is some risk that even a feminist could read "she is very interested in advancing women and other minorities in the STEM field" as a bit of a consolation prize. Again, write the strongest letter you can.

Answer to the question in the title:

"yes" if and only if feminism is a matter of the person's research activity.

("No" if it's not.)

Reason: you wish to say that this person is an excellent scientist. Period. The person reading your letter doesn't even need to be informed of the candidate's gender, let alone whether they hold feminist viewpoints.

(EDIT: This answer assumes that the honor program is about science rather than anything else like social or organizational skills. Please consult other answers if this assumption does not hold.)

I would approach this with extreme caution, and honestly, I'd be quite hesitant to mention it in a LOR I was writing, despite finding your student's objectives laudable (and being quite comfortable being described as a feminist). There are a few reasons for this:

• It calls out her gender. Very rarely do we write about the commitment of a male graduate student to the representation of women in STEM fields. As much as I hate to say it, even mentioning it will bring the gender of the applicant to the forefront, and there's pretty strong evidence that a female applicant is inherently disadvantaged.
• There are two audiences who care about this: People who care about women in STEM, and people who will go "I don't want a feminist/political activist/etc. in my lab". The former will likely still be interested in your candidate - after all, if they care, they should be caring about her scientific accomplishments. The latter will likely hold those actions against her.
• Along those same lines, it gives someone the opening to dismiss her as "What, she doesn't do good enough science for you to just write about that?"

Basically, I think mentioning it can only really hurt her, unless the position clearly calls for evidence of that kind of advocacy work, or you know it's a passion for whoever would be reading her letter (for example, if you're writing the recommendation not for a program, but to a specific PI).