Hands Across the Aisle is a broad-based group of women coming together out of concern of the erosion of women's rights, women-only spaces, and women's boundaries generally. The group encompasses feminists, conservative women, religious women, etc. And the group's purpose is to 'reach across the aisle' and find common ground with each other with regard to what is seen as a threat to women's rights.
The group is probably US-heavy, but includes women from all over the world. It is not "an offshoot of the Heritage Foundation, a Republican thinktank".
But, to a degree, like FWR here at MN, women who were not previously exposed to, or had interest in, feminism generally, have woken up to what is going on with women's rights, and they are rightfully worried, and now have more interest in feminism.
I have always stated that feminism is neither 'left nor right', because they are descriptors of men's politics, and men from the left, and men from the right, almost all participate in male supremacy and all of them benefit from it. Feminism stands outside of men's politics - it has to.