I've read this thread with interest, as I know a fair bit about attachment theory and am both interested and often horrified at the ways in which it's traduced in popular understanding, particularly in the context of 'attachment' parenting which - while I'm sure it works well for some families - has no meaningful basis in science.
The lack of real evidence for AP as a method is not necessarily a problem - parents can and should raise their children how they choose. The only time it is a problem is where the proponents of a particular method, such as AP, try to imply that their chosen approach to parenting has some kind of evidential basis. This is noticeably the case in popular discourse around APapproaches to infant care where studies from attachment science are frequently misquoted or selectively quoted, in order to imply alarmist conclusions in support of that approach. As a PP said, where an ideology claims a scientific rationale but does not in fact have one, it invites curiosity about whose agenda that ideology might benefit.
I think the way attachment studies have been appropriated - without real justification - for a highly moralised discourse around childrearing, which is largely deployed by and aimed at mothers, absolutely is relevant to feminism.
The sociology nerds on this thread might be interested in fairly recent book on Parenting Culture Studies, which looks at attachment parenting as part of a larger enquiry into our modern, anxious and expert-driven parenting culture. While it's not an explicitly feminist book it raises a number of very interesting points about the discourse of competing 'parenting styles', the 'experts' that promote them and the ways in which these de-skill parents (mothers in particular) and actively work to undermine parents' ability to support one another, as relatively trivial differences in approach become a social and interpersonal minefield.
In summary then I think whether you consider AP to be exceptionally antifeminist depends a bit on your stance and understanding of what it means to be feminist. But it is part of a wider phenomenon - expert-driven parenting culture - that I would argue really is antifeminist, or anti-parent really, as it invades family life, deskills individual parents and undermines the ability of families to support one another by creating artificial 'parenting style' barriers between them.