If professing Christians followed Paul's instruction on how to respond to someone who is offended by what we eat, then the proper response would be for others to not eat animals in the presence of vegetarians.
Any of us who have been to a church event where food is served know that the opposite happens. Instead of being concerned about our sensibilities, we are mocked and pretty much cast out while the crowd stuffs their faces with dead animals. This is not a true Christian response and we all know that.
Instead of taking that teaching in its context and having respect for those who do not eat animals, it is used to justify eating meat, which is not the spirit of the teaching at all. They take it and twist it to their own advantage. 1 Cor 8:13 is the Christian response.