I find soy milk neutral in tea. If I now put dairy milk into tea, I find it has a strong "cow" flavour.

Modern dairy farming is very intensive and polluting. (It also feeds the meat market, most of the cheaper supermarket cuts being dairy cow or heifer).

Yet I'm not suggesting people should boycott cows' milk and derived products (unless for personal health reasons). What is objectionable is the amount of marketing/advertising/packaging/shelf space devoted to small volumes of low-quality milk turned into various yoghurts and other more or less fermented products, creamy desserts, and intestinal stimulants, sold at high prices : industrial dairy production feeding straight into a marketing-based food industry sector. I don't know what the ratio of raw material to abusively "manufactured" added value (the marketing, ads, packaging, merchandising) in the cost price is, but the  continuous pressure to bring down the price paid to the dairy farmer leads directly to increased intensification and the debasement of the product. Better-quality producers and products, such as traditional cheeses, are increasingly marginalised (even in France).

But, as with meat, the marketing works. It's not easy to see how to turn the situation round.