Exceeding the planetary boundary for species and biodiversity loss alone can make the Earth uninhabitable for humans. The metric for the Planetary Boundary according to the Stockholm Resilience Center is extinctions per 1 million species per year . The current extinction rate exceeds this limit by 1000% - 100000%. .
The effects of a shift to a plant-based food system on species extinction and biodiversity loss are not directly quantifiable. The causes are diverse and mostly interacting. However, the main cause is land use change. 3% of global land use change occurred for villages, cities, and roads, 21% for crop production for humans, and 76% for animal agriculture. Animal agriculture is by far the largest direct cause of habitat destruction. With a shift to a plant-based food system, 74% of all anthropogenic habitat uses can be reversed. In addition, without animal agriculture, fresh water use, emissions of eutrophying and acidifying substances, pesticide use, and wildlife trafficking all decrease sharply.
The links between animal agriculture, species extinction, and biodiversity loss are detailed here and here.