Can you be on the right (as in be an anti-immigrant nationalist who believes that Islam is incompatible with secular liberalism) and still be a feminist?
Yes. It does not usually happen (most nationalists also think women should be forced to have babies for the fatherland) but considering that feminism, per definition, is about liberating women from patriarchy, and not about being a generally nice person (liberal feminists tend to be a bit confused about that) I'd say it is possible.
Though I suppose sooner or later such a person would have to decide what is more important to them.
Liberating women while working inside some small country instead of networking internationally is not really possible - a liberated society surrounded by patriarchies would soon be invaded by those patriarchies, as they have more military and more population, period.
But I do think a woman can be unaware of that latter fact and truly mean to liberate women while holding nationalist views.
A woman can also be a feminist and feel that anti-immigrant nationalists are the only ones who take her concerns about women's safety seriously.
As for believing that Islam is incompatible with a secular society, there's actually women with Islamic backgrounds who hold that view, and not for lack of information, I'd imagine.
As for the woman described in the article, it seems she's just desperate and feels she has to prioritize the fight against immigration even over feminist struggles.
I think she's wrong to do so, but I can see where she's coming from.
There's just no large group that is unconditionally pro-women, and sides with women, always.
You have the choice between right-wing, where you have to deal with all the oppressions you are currently subject to, but can hope for no more to be introduced. Or left-wing, where you can hope to have some oppressions removed, but also a high risk of being oppressed in new and inventive ways. (Men in women's spaces; Muslim men being misogynist in different ways, etc.)
Either you join neither side (then you are on your own and that feels shit and is dangerous and unsuccessful) or you choose the lesser evil.
I suppose as a lesbian, unwanted pregnancy is not such a risk for her, and since the anti-choice agenda is the worst thing right wing want to do to women in the near future, it makes sense she chooses that.