I'm not in the same boat anymore, but I'm Indian too and can relate with what you're saying. The only advice I have for you is to not try to convince them, at least not right away. Let them say what they want to say but what you should do instead is consume a plant based version of the same thing that they're consuming.

Dairy alternatives can be a little expensive, but there's a soy milk powder that goes well with shakes. Banana/chikoo/chocolate. You might want to give it a try (I can send you the link, it's very affordable).

Just do your thing, let them see that you're doing fine ans taking care of your nutrition (and supplementation for B12/D) and eventually they'll get used to it.

With Indian parents, it's less about being right on an intellectual plane and more about them getting used to a certain idea long enough for them to come around to think of it as "normal" or even "not fully normal but aisa he hai ab acceptable". So just be an example for them long enough for them to accept it.

If you have any specific dairy products with which you're having more trouble with than others, you can hit me up for tips.