Two people falling in love, belonging to different castes or faiths commonly have these issues when it comes to the point of consent of families for marriage.
It is not easy for parents and close family especially from the girl's side to agree easily. It's human nature to think about the adverse effects and struggles faced by such marriages and the people in it.
It is NOT easy to raise a girl child, cautiously watching over her so that she has her freedom and yet she doesn't discredit the family. Here the girl's parents and relatives might feel let down as their daughter is planning for an inter-caste marriage and it slipped their attention.
Added to that is the worry and apprehension about being rejected by the family circles. This is more if there is a younger brother or sister of your girlfriend who is yet to get married.
First, both of you have a serious discussion about life after marriage and the realities of job, place to live and finance at hand, resources for having and raising children, etc. Then assess the commitment of both of you to go through the marriage after fending off many hurdles. If both of you can make it together, then have a discussion with parents on both sides and try to reason out their fears.
Show that you are committed to the wedding and keep their daughter happy. This may need few discussions, wherein you layout the plans both of you have for a career, source of money/salary to run the family.
Agree on a timeout, give a month's break for all of this to sink in. The re-start the discussions. Then give a time limit for the girl's parents and relatives about marriage with their consent or if needed without their consent. If both of you are committed and firm, they would understand your commitment and the patience you have shown and would agree.
If they still don't agree, then take decision for the marriage and as time goes by, things fall into place. Please remember that the struggles of life with test the limits of love that you both have and there should not be any doubts about the trust and bonding between you two. Best of luck.