My understanding is that there is no bright line in linguistics and that language definition is by default messy and political

It's not really by default, more like by necessity. Almost all categorization schemes for human cultural artifacts are necessarily blurry at the edges, and just because someone has provided a definition that is useful for one purpose (the study of linguistic differences across cultures) does not mean that it is suited for another purpose (rhetorically implying solidarity or separation between two sets of people).

Mutual intelligibility is the standard criterion, and by that standard, there are different 7-8 language families in China.