Disclaimer: As in all halachik discussions, what appears below is not meant as ruling, but as discussion only. Please discuss any practical applications with an orthodox rabbi.
This post is in honor and memory of my Rebbe in halacha, Rabbi Shemuel Kedar of Ofrah, זצ"ל. Rav Kedar passed away on Sunday, א' דחוה"מ סוכות. He taught me more than I can impart, in all aspects of life. I already miss him terribly.
Background information: It is not only forbidden to eat milk cooked with meat, but there is also a Torah prohibition to cook the two together. Human milk (female), however, is not considered chalavi (halachik milk that is forbidden to be cooked or eaten with meat). It is rather neutral (parve). Chicken and other fowl are considered meat fully, even though their categorization as such is of Rabbinic origin (see Chullin 116a for the whole story.) We will refer to meat of Torah origin as 'meat', and Rabbinic meat as 'fowl'. Animal milk products will be 'milk', while human milk will be 'human milk'.
The Rashba (ad loc) adds a restriction on cooking meat in human milk. He forbids this because of mar'is 'ayin, an impression of impropriety. One who sees the act may mistake it for cooking actual milk with meat. Within reason, we are careful that no incorrect conclusions be derived from our actions. The Rashba does not distinguish between Torah or Rabbinic prohibitions in his system of mar'is 'ayin.
The Shulchan Aruch (Y.D. 87:3-4) quotes this Rashba. The Rama writes that people make 'milk' out of pressed almonds, and place it in fowl dishes. This is fine, because the fowl is only Rabbinically prohibited to be cooked in milk, and we are not concerned with mar'is 'ayin for Rabbinic prohibitions. However, if the dish is meat, then it would be problematic to cook in almond milk. Therefore, one must display almonds with the milk, so that it is clear to all that this milk is not real. In the same vein, although Rama forbids cooking human milk with meat, if that meat is fowl, it is not worrisome.
The Rama seems to agree with the Rashba. The Rama wrote Toras Chatas as a place to examine halacha in more detail. There, he sharply questions the logic of the Rashba. He says that mar'is 'ayin should only be considered where the Torah prohibition seemingly broken would be one that carries a punishment of Kares, excision from the soul of the Jewish Nation. Any less, should not be considered for mar'is 'ayin, and therefore, should be permitted. Therefore, meat in human or almond milk should be permitted.
The Kreisi Upleisi agrees that almond milk should be permitted completely, but for a different reason. He holds that mar'is 'ayin is only considered where the ingredients are true meat or milk, but permitted on halachik grounds. For example, human milk is obviously physically milk. It serves the same purpose and has similar ingredients as animal milk. The fact that it is parve is a halachik distinction, not a physical one. Therefore, mar'is 'ayin applies. However, pressed almond juice is certainly not real milk. The term is borrowed because the substance is white and viscuous like milk. In this case, no mar'is 'ayin should apply. (Red wine is not forbidden to be placed in a dish, just because it looks like blood.) Also, since it is generally known that almond milk looks like milk, but is parve, it would be permitted.
Shach rules against the Toras Chatas and Kreisi Upleisi, and holds that even almond milk in meat is forbidden, as ruled practically by the Rama. He also rules as the Rashba and Shulchan Aruch, that mar'is 'ayin applies to Rabbinic prohibitions as well as Torah.
Rav Ovadiah Yosef (יחווה דעת ג:נט) permits drinking non-dairy creamer in coffee after a meat meal, because eating milk after meat is only prohibited Rabbinically. However, those who hold like the Rama would be hard-pressed to find permission to eat parve margarine or milk with their meat meal.
Rav Kedar זצ"ל (in his שו"ת, p. 114-115) speculates to permit this even according to the Rama (he does not conclude leniently for certain). He uses the Kreisi's idea that the creamer or margarine is generally known to be parve, so there is no mar'is 'ayin. Also, he mentions the Pri Chadash, who placed a moratorium on creating new mar'is 'ayins that were not expressly forbidden by the generations of old. Even though he accepted the Rama's prohibition on almond milk and fowl, he would probably permit margarine or creamer, or even vegetarian meat, that is parve.
Again, the above is not meant as ruling, but as discussion only. Please discuss any practical applications with an orthodox rabbi.