The rationale behind some of the kosher laws can be complicated and tricky. The thing about soy milk, coconut milk, almond milk, and so on is that no one would logically confuse this kind of milk with cow’s milk or goat’s milk. In the case of the prohibition of chicken and milk, one might logically confuse fowl with meat from another animal, and thus think that if chicken and milk are permitted to be eaten together then beef and milk can also be permitted since both chicken and beef have to be koshered (draining the blood with salt) before consumption. The regulation pertains to the potential confusion of the dietary law in the mind of some rather than scandal that might arise if another were to see you drinking soy milk with meat.
Further, although the Torah prohibitions generally apply only to what is EXPLICITLY mentioned in the Law and not to what may be omitted, there has to be some kind of generalization when potential confusion might result due to excessive specificity. For example, the injunction in the Torah is not to boil a kid in its mother’s milk. If one were to interpret this as literally as possible, then it would apply ONLY to a KID that is BOILED in its OWN mother’s milk. This would mean it is permitted to eat a kid that is boiled in ANOTHER mother’s milk, as well as any OTHER animal boiled in its mother’s milk, whether kosher or not. This would create tremendous confusion in the already complicated dietary laws.