I think that some kids get bullied for anything - the size of their shoe, the colour of their jacket etc. It's shit, but it's not on you.
DD's BFF's parents were 19 when they had her. friend hasn't had any issues although the friendship group do like to discuss how big he potential gap between her and any future siblings might land up being! Mostly because they're jealous because none of the other parents are even vaguelly considering a new baby (they're all 10). 
the mum did tell me that she found the first few years quite difficult and SHE felt very self conscious at school events etc, and she had some issues where she felt the school didn't always take her that seriously. But I think that was a mix of genuinely happening and her being self conscious.
I'm actually one of the older mum's in DD's year group becuase I was a bit older when I started and there's a big gap between DD and DS, and DH is even older and is fully grey. So DS got a bit of teasing for that, but I don't think ti was major.
With BFF's mum we are friendly and have been out a few times and I like her a lot. But we're never going to be BFF becuase the gap is just too significant in terms of life experience etc. DD finds it hilarious that me, and even more so DH, could be BFF's grandparents!