Hmm..if you don't want to argue...you could always show your research in an unbiased way. Like Shadowknight said, it's just by product of cheesemaking. Nothing chemical at all.
I remember when I was discussing how butter is not a processed food with my dad. Technically, it is -it requires processing; however, this processing is 1. get milk 2. churn it 3. collect later. Nothing bad about it.
You could also collect positive benefits of whey protein. As well as saving budget and helping you gain muscle mass, it also has positive health benefits. A quick google search tells me this: Whey Protein Benefits, Risks, & Top Picks - BuiltLean
Tell them while you understand their concerns about it being a gateway drug (I think they are imaging that you'll start chugging the stuff while taking steroids and getting swole. There are negative connotations surrounding sports drinks; too right, some of them are junk. Whey isn't) you have done your research and reached the conclusion that this would aid you; also, since you care about your health, you would never take drugs or anything that would cause harm to your health. You're very intelligent, and they know that. Hopefully they'll understand.