There are dozens of branches of feminism and movements within them. While there are major differences and some put more emphasis on agency and choice than others, none of them really define something to be feminist just because a woman chooses it, reasonable or otherwise. Something being un- or anti-feminist doesn't mean it's automatically bad for the individual or that people should be forced or oppressed to meet a particular standard, it just doesn't further the objectives typically given by one or more branches of feminism. Buying clothes from a shop with likely dodgy parts of their supply chain that often impact women more greatly in the textile industries than men likely involves unfeminist elements. Plenty of daily choices most make with the options available don't further those objectives. It's an observation, using it or taking it as a stick is separate from that.
The idea that disagreeing with one element of a tradition of questionable origins that can hardly be pinned down anymore means that one shouldn't have any element seen as traditional is a bit laughable. White dresses are a fairly new tradition comparatively and more connected to class though weird virgin ideas got attached to it in some circles. Plenty have traditions of other colours. Even in the Victorian times where the white dress as we know it now came from, there were many other colours that were seen as good or bad to get married in.
As for my wedding, neither of our fathers were involved in our wedding, I'd met his once and he met mine once the month after we married. We both wore blue as they were our best clothes, he wears a ring and I don't as jewelry aggravate the joint pain in my hands so I don't wear rings or bracelets, and I changed my entire name soon after. So, we didn't really take any of the traditions forward, but we did get married, I was 18 at the time and had spent time living with and caring for his mum and step-father, and I immigrated which while it provided me some protections I would not have otherwise, it did and continues to put me in a more vulnerable position in terms of employment, finances, and certain legalities compared to him being an immigrant spouse from that age (the age was raised not long after I did so, but younger wives particularly are often more vulnerable). I've no idea how that stacks up ideologically with different branches of feminism and I don't particularly care, but while considering and changing traditions has always happened and questioning them can lead to better things, I agree that these are pretty small fries when it comes to liberating women from social disadvantages and sexism and I don't see a father walking with his daughter down either an isle (holiday wedding?) or aisle as something to invest a much energy against.
I did hate having to have my father's name and occupation on the certificate (I wasn't sure of the latter and only realized later his name is misspelled which amuses me a bit) but I would equally if not more hated having my mother on it with her hatred of marriage and me. It does feel in this age with so many ways to check identity that things like that or the 'acceptable profession' references for passports and things are out of date and I don't think tradition or future generations potential interest in genealogy is a good enough reason to keep that.