Inter-caste and Inter-religious marriages are no longer a taboo. A lot depends on the level of education, social and monetary positions and the family background of both boy and girl.
26 years of age for a boy, I think is on the younger side to fully understand the consequences of a fallout between you two or between the two families. If you are in a relationship for 4 years with the knowledge of the elders, then I'm surprised that there are objections because to the outcome here was obviously a long time back.
Firstly convince yourself - it's not infatuation but true love, dreams are different from reality. Then the same from the girl's side. If both of you are sure that you two are committed to a lifelong relationship and ready to overcome hurdles together then you can think about marriage.
Secondly, what is the level of education or work that both of you can do or currently do? Getting married and riding into the sunset happens only in the movies. The expenses involved in running a family (rental, travel, household, food, clothes) and support a new addition (child) are quite high if you have to support each other on your own.
Thirdly every boy and girl will believe that parents will eventually agree after a few months or after the arrival of the first child. But here again, there are some other factors that get involved and force parents to keep aloof even if they like you.
Fourthly, try to get an idea of what is the fear of the girl's parents, is it that they will be social outcasts, does the girl have a younger sister or brother to be married, do they come from a very conservative family or a town where in this intercaste marriage would be a major blow to their standing in that particular neighbourhood which the girl's parents cannot withstand.
Try talking to them about the good between both of you and your commitment over 4 years and find an elder who can be a go-between both your families. This may take a while.
If things don't change and you still are committed to each other, then convince the girl for marriage, if only, if only that you honor your word that comes what you will do everything for the marriage to work and not abandon the girl later on for whatsoever reasons.
Lastly look at your financial situation, friends whom you can count upon, as if you do get married against family wishes, then you need help at hand to support you both at the time of need.
Discuss all these with the girl's parents and give an impression that you have really thought about everything long-term and will be looking after their daughter following their own traditions.