The IPCC, FAO (UN), and the World Resources Institute put emissions from (all) agriculture at around 20%-25% of total emissions.
This article cites a single paper in opposition, which claims that emissions from animal agriculture are more than double that number. I don't have the time or expertise to comb through that paper with a critical eye, but the reports of the above organizations cite dozens of studies so it seems the weight of evidence is tilting towards the 20% figure.
This isn't to say that animal agriculture isn't an issue - it's a huge issue, and not just for the climate. But I think it's important to acknowledge that these emissions numbers aren't widely accepted.
Thank you for sharing! I'm a big proponent of the planetary boundaries framework, it's a great way to visualize overshoot. While climate change is a big (perhaps the biggest) issue facing global civilization right now, it's extremely important that we don't get tunnel vision and try to solve for one variable without looking at our biosphere holistically. (That's how we get carbon capture and geoengineering.)
A few more links/resources for those interested: