I could understand it better if your dc were getting a birthday gift from you, but no present from you and no presents from their friends seems mean, frankly.
I really hope you are right that your dc are truly happy with this arrangement, but I am absolutely sure that I would have felt dreadfully unloved if my parents had done this - my birthday is just before Christmas, and my parents did try to keep the two separate, so my birthday felt special. It was only when I wanted a pair of boots that was too expensive to be just for my birthday that I had a joint Christmas and birthday present.
My mum was also very good at guilting me into things, and making me feel like I couldn't tell her my true feelings - one year, the main present in my stocking was yarn and knitting needles so,I could knit a scarf for my dad. I did actually dare to tell her that I thought this was unfair, and it was a present for dad not me - and she offered to give me some money instead, but then guilted me into keeping the yarn etc 'because your dad would love to have a scarf that you knitted for him!
It is always hard for a child to be the one who is doing things differently, and I always worry that they will resent this, especially when it is due to their parents' beliefs, not their own. Your family is your safe place (or should be), and I worry that children won't challenge their parents on things like this, where it is based on their parents' deeply held beliefs, because they are afraid, on some level, of disappointing their parents or making them cross, and thus making the foundations of their security unsure.