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Actually, is quite simple. 

The first thing you must take into consideration is:

-What kind of Milk are you offering?

If it says "Mix" then it will be rejected by everyone. You must interact with the collector and then select "Flush". 

But, if it's labeled with FapetAxFapetB names, then you must search for a NPC that likes that kind of Fapet. For example 

You got BunnyxKelpie Milk. Now you must find a NPC that likes either "Bunny" or "Kelpie" milk, anything other that that will be rejected. 

For Story Mode players, they must first interact with the NPC and then pay attention to what they says and see what kind of Faper they do name.

 "Shoo, Kepie/Bunny, Shoo" "This disrespectful Bunny/Kelpie" "I don't want to talk with a lowlife Kelpie/Bunny"  <- This kind of text means that this NPC is selectable to Sell/Gift Milk that you have. If they name other species, they will reject you. 

Now you have to:

-Press the Middle Mouse Button to aim to the NPC

-Press 1-2, to select the Milk Cup

-Hold Right Mouse Button, and see the Menu Appears (If it doesn't appears, either the target is incorrect. If not, press F5 and try again) 

-Move the Mouse Pointer to the preferred option, and release RMB. 

Hope this helps. More information about this kind of mechanics are found on Tab>Book>Help

Completely agreeing with @MartPriest. 

- The use cases for 'Mix' type are mostly to self drink and gain the according boosts. I'd recommend getting all milk cups (if you have much of it stored), then flush the rest to get a clean milk combination in the collector

- "how many types of milk there are?" : the same count as current tamable fapets (except goblins), they are assigned on random from the list of known tamings.

A side note, upcoming update will have icons above quicklots, representing current mix (Fapet A , Fapet B, or mix) :3