@agowa338 no native english speaker would think you were talking about some unnamed idiot in any of your examples.
It's clear from the sentence structures that it's a name of a thing in its own right, even without capitalising it.
If you *were* talking about some unnamed idiot, you'd say
"we use that git for that"
"we'll have to check with the git"
"a git said abcd"
"according to some git"
"something is wrong with that stupid git"
and so on.
well think of most of these statements as shortened sentences from chat messages instead of something said within an E-Mail or something.
Also I'm not just working with native speakers. I'm dealing with people from all around the world basically. (Ok, it's mainly Europe + India + USA, but still)
Also now think I'm referring to a specific person and not "some random git". Like e.g. I'm talking about you to a coworker.
Then it for sure would be "we'll have to check with git for that". It'd be extremely impolite, but the sentence structure would technically be correct in the case where one'd use "git" basically as ones 'alias'.
I mean if grammar-wise saying "[Our] manager said", "Our expert said", ... then for sure "Our git said" is also valid.