Not my experience (in Germany). Sometimes people (mostly women) assume I am taking a day off for daddy time and give me some sort of mini applause. But that is pretty rare.
More notable is perhaps the gender distribution on the playground. I do think it is easier for moms to connect/bond with each other. Like if I plan an excursion and wonder what friends of my kids could join, I find it more difficult to simply ask another mom. Might just be me, though.