"Snobbery" is not limited to cycling
You can find it in every sport - in everything. Hell, I'm a curler and avid badminton player and there are even snobby people in these sports.
The fact is, it's just a part of life. There will always be people who will look down on you. My best advice would be to use it as a reason to excel, as a reason to improve and better your skills so they can no longer look down on you