Do you consider the relationship of two molecules of water to be similarly coincidental or along a continuum from e.g. the nature of two elections all the way to how two universes might be similar? I figure fundamental particle nature is less coincidental than human nature, which is correspondingly less coincidentally related than two heterogenous dust clouds.
I don't see any reason to have a strong belief about why any fundamental constants are what they are. This is so far beyond what even our best physics can say anything meaningful about that I feel an obligation to studiously have no opinion about it.
I will say that I see no compelling reason to believe that the values of fundamental constants are NOT just random.