This law has a direct connection to the cheese prohibition: rennet, being a separate milky substance in the stomach of a ruminant, should not make the cheese prohibited. When Rabbi Yehoshua avoided saying the reason why the cheese of idolaters is prohibited, he did so because a year had not yet passed since the decree was promulgated, and he did not want people to argue about its reasons. That is why he hinted at a kiss that seals the lips. The two most prominent reasons are the snake venom in the milk and using the actual meat part of an animal (maw). Tosafot say that now the snakes are not prevalent and the cheese is permitted, but Rashi and others disagree.
Art: The Snake Charmers, Bombay by Edwin Lord Weeks