The Algorithm has been serving me a lot of “What if [character from other franchise] was in WH40K?” fanfic readings on YouTube, and I've been listening to them as background noise at work. That naturally made me wonder how monkey foxes would fare in the grim darkness of the far future. I'm not sure it would go well. Just as a comparison:

Imperium of Man:

- aliens must be purged

- innovation is heresy

- spans the galaxy

Yinrih:

- aliens must be sought out and welcomed

- innovation is worship

- confined to one star system

Most yinrih would regard the Emperor of Man as another lichlord. Some flavors of Misotheists would go all in on chaos worship. The more superstitiously inclined would see the demon-infested immaterium as confirmation that the Underlay is in fact hell, and in this case they may be right.

Yinrih tech is far beyond that of the Imperium, albeit without mass interstellar travel. But the Imperium has sheer numbers. Focus MIGHT get along with the Tau depending on what part of Tau fluff you pay attention to.

Yinrih would not see the Tyranids as sophonts and thus not attempt to introduce themselves, but they would likely attempt contact with the Orks and it would not go well.