I didn't have a phone until I was 16 despite most of my peers getting one around 12/13. I didn't get bullied for not having a phone, in fact no one really made any comments on it other than an occasional "wow, I couldn't live without my phone!"

Granted, this was over ten years ago, and was probably the first generation of teenagers where cell phones were near-ubiquitous. I don't know if kids nowadays would get bullied just for not having a phone, but it would severely limit their social interactions. Riding your bike and knocking at your friends' doors randomly, or going to the mall and expecting you'll find some people you know there, these are from a bygone era.