That can be true of lots of distasteful, but necessary topics necessary for life. I don't usually engage in small talk about mortuary science, sewage treatment, or surgical removal of tumors, but all of those are certainly incredibly important to life as we are biological animals ourselves.

Yes, but we have experts for these topics, like we also do for animal agriculture. It's just that the broad public has relatively much knowledge for certain topics, like sports, whereas it's quite natural that most non-experts are relatively ignorant of less sexy topics. That's all I wanted to say with that, that I'm not berating anyone for not being an expert here.

Assuming the sheep are only fed from the grass they eat on-site, how are they NOT carbon neutral?

You're correct that they take in the same number of carbon atoms as they eventually exhale/excrete/etc.. So, in that sense, they are carbon-neutral.

But that doesn't mean they're climate-neutral, because when you combine carbon atoms with 4x hydrogen, you get methane, which for physical reasons has a significantly stronger greenhouse effect than CO2.
And ruminants (like sheep and cows) belch out lots of methane: https://en.wikipedia.org/wiki/Ruminant#Ruminants_and_climate_change

That's why even people who would immediately choke to death, if they ate a vegetable, could still help out on the climate front, if they switched from beef (and mutton) to poultry and pork.
See this graph, for example: https://ourworldindata.org/explorers/food-footprints

And yeah, reading through the article, I'm happy that it's being used for solar, I'm happy that if we're already raising sheep, they're at least being used relatively efficiently, I'm even happy that the sheep are living a relatively happy life.

What I'm less happy about, is that OP vegan was pretty spot on.
They're raising additional sheep for this endeavour. And no one had the expert knowledge to ask, if the belching sheep maybe somewhat undermine the climate advantages of solar.