Part of the problem is referring to things as "girly" probably
I never watch girly shows. I find men who do to be truly, truly outrageous.
I've been a huge Sailor Moon fan for the bigger half of my life, and I never really felt the least bit emasculated or ashamed by it, even though it clearly is a franchise with a young female audience in mind. Actually I find that when it comes to anime I've always been way more interested in the "LOVE AND FRIENDS AND MAGIC AND PRETTY AND SPARKLES" stuff for girls than the stuff intended for boys. The same applies for Disney movies. Nearly all my favorites are singing princess films.
I think the primary reason for your aforementioned "paradox" is the fact that Totally Spies and many of these other girly franchises are created and controlled by men. It's kind of the same as when you're watch a show aimed squarely at young kids and then suddenly there's some joke or reference that no one under the age of 30 would possibly get. Partly because they want to throw a bone to those outside their main audience, and partly because they're adults and they want to stick something that appeals to themselves in their work, even if their demographic isn't the target of said work.
I like Kung-Fu.