Actually you could eat vaccines with no problems (unless you tried to eat the syringes too) but it would be a waste.
Stomach acid and digestive enzymes will just deactivate most components. Live vaccines might cause issues (probably wouldn’t want to drink the TB vaccine). The post in discussion shows a shocking fundamental misunderstanding about how all of this works though. It is meant for like-minded people who would accept this logic.
It makes me wonder if there are any substances that are safe to inject straight into your tissue that your body would even notice–let alone kill you–if you ingested in the same quantity as an injection. Icky taste aside…
Maybe some compound that is relatively harmless on its own but yields a toxic compound in contact with stomach acid? Blood is slightly alkaline so it would not trigger after an injection and leave time for the kidneys and liver to degrade it. Maybe some cyanogenic glycoside?