If you cook a meal from both meat and veggies, it becomes "contains meat". https://steamuserimages-a.akamaihd.net/ugc/1841408985877046221/BA2A13DE84F6B82364059E4A4C2DB7F783CB1331/
If you cook a meal just from milk, it's suitable for everyone. https://steamuserimages-a.akamaihd.net/ugc/1841408985877043622/B370EB29AE3C2FDA2A1C818F733D666A324A24EB/
If you cook a meal from both milk and veggies, it becomes vegetarian instead. https://steamuserimages-a.akamaihd.net/ugc/1841408985877045870/391C0033D15198553381D19260CADA1A0AB10DFF/
I would expect milk in meals to always satisfy the "Meat eating" precept, as it describes "Eggs, Milk and processed foods are fine". It seems to only do so if it's the sole ingredient.
Thanks for the bug report, I'll send this into the devs. I've confirmed it in 1.3.3235. This one may be trickier because milk needs to go both ways. I spoke with the devs and we think we have a direction on where to go.