Is that a lot or a little compared to a high polluting company?

It's about 1/7,000,000 of global emissions. Less than any country I believe (except maybe Vatican City, but that's not listed on this map). Larger than many small towns and airports.

Has to depend on how you allocate. If you count Catholic Church funding of overseas missionary trips and allocate those all to Vatican City, it probably ends up pretty high or maybe not "high" but at least not the lowest of all countries. If you allocate them to the country of origin of the donations, then probably not.

Sadly most of the datasets I'm seeing lump the Holy See in with Italy.

An interesting breakdown would be "carbon emissions controlled" - the US "controls" way more emissions than the US directly makes, as so many emissions from other countries are direct results of US spend.

Those emissions would mostly be counted in the airports on this map.

This is one of the things you have to be careful with data like this - pollution can be counted multiple times, especially if you are comparing different datasets.

Okay, but how does it relate to the original question? According to the website for the OP, I could easily find feedlots/industrial sites with co2 emissions that are orders of magnitude higher, so I'm going to conclude that no celebrity's emissions gets anywhere near "fractional percent of industry".

To be fair, that's just one wealthy person right? Curious to know the total output of the 1%.

I don't support a "name and shame" approach, but if I did then I think this would be effective. That's essentially what it is now, just targeting corps. Celebrities have a massively higher amount of power than non celeb people, and higher power than most corps. Putting the spotlight on them would be effective.