I also think you acknowledge her birthday with a quick "happy birthday" text, but don't acknowledge your anniversary. I'm not an expert at this though, but I'm looking through a different lens...she knows that you know it's her birthday. No divorce or separation or fighting between you changes the day of her birth. I think if you ignore it completely, it makes it obvious that you are intentionally ignoring it. Just like taking the pictures down, I think sometimes you can look desperate/trying to make a statement rather than just be genuine.
