Accept him whose faith is weak, without passing judgment on disputable matters. One man’s faith allows him to eat everything, but another man, whose faith is weak, eats only vegetables.
For starters, Paul is not saying that vegetarians are weak Christians. That is not the context of the passage.
What Paul is saying is that there are some people who do not have a good understanding of the Bible. The obvious solution would be to teach them right from wrong and guide them into making proper choices. But in the meantime, we must coexist with people who do not understand the Bible as they should.
Throughout history, Christians have been well intentioned in prohibiting certain activities. Some of these prohibitions have been based directly on scripture and others are made up because of the possibility of taking an activity too far.
Dancing was once an issue within the church. Even outside of the church, values were different in the 1950’s than today. Elvis couldn’t be shown from the waist down because the wiggling of his hips was considered too sexual.
For some people, there was no temptation from seeing this and the prohibition was unnecessary. They had mastered this sin and their conscience was not violated. Others who were weaker needed to be protected from themselves or so the thinking was.
Ultimately, we are all at different levels of faith. We should all strive to understand the Bible and apply it properly. We need to realize that not everyone is on the same level as us however and what does not violate our conscience may for them.