I don't drink dairy due to intolerance and I find it disgusting possibly for the same reason. I also don't like any milk substitute so I'm out of any target demographic anyway.
However, as far as I know according to traditional Chinese medicine milk is considered a big no no.
I don't rely on it but I do get acupuncture from time to time. My wife is a tcm practitioner and I can vouch it works. I don't claim it substitute western medicine but it works very well along side it.
Try eating shredded carrots with coconut oil, olive oil and salt on an empty stomach once a day. In a couple of weeks try drinking milk again. If your milk intolerance is due to a bacterial overgrowth you should be able to tolerate it after that.
Carrots are an indigestible fibre so they carry the coconut oil into your small and large intestine. Usually the coconut oil would be absorbed rapidly. The coconut oil then kills the bad bacteria lining your gut. The carrots on their own also absorb some of this bacteria and are excreted. You can do the same thing with bamboo shoots if you don't like carrots.
The evidence for this specific effect is pretty weak at the moment, but it's all good natural food anyway so you have nothing to loose. It worked for me so I'm passing it on.