Money is a record keeping tool.
In a theoretical pre-industrial society, there could have been granaries for Chickpeas or other edible dried food items.
When farmers put their chickpeas into the government granary, the granary overseer would theoretically give the chick-pea farmer one or two copper coins. Many months later, when the farmer theoretically gets hungry, and there are no chick-peas to eat outside of the granary, the farmer could give the copper coins back to the granary overseer in return for the grain he or she deposited.
Many years later, you could put metal coins in a bank in return for pieces or paper or certificates of deposit. The paper could be brought back weeks, or months, or years later and redeemed for the metal coins.
Essentially, workers receive money when they work. Workers lose money when they buy food, clothing, when they pay for medical services, etc...
In theory, money could measure number of hours worked. When people grow rice, dry out the rice, make bags, put the rice in bags, it takes time. The price of a bag of rice can be modeled as the number of hours every person who touched that bag of rice put into preparing the bag of rice for other people.
Money could be used to record labor hours. A worker spends 40 hours making cardboard boxes in return for 40 hours of other different people growing lettuce and working to refine petroleum into gasoline, etc...
When you asked whether or not the economy would collapse when and if the people of the world stopped eating meat, it sounded like you thought the economy was more than mere record keeping.
Suppose that you write down how many carrots you have inside of your refrigerator. Every time you buy groceries, you add a number to the previous total. Every time you eat a carrot, subtract a number from the previous total.
Eventually, your record of carrots might be incorrect. Maybe 10 carrots are inside of your refrigerator instead of 19 carrots.
Money won't make potatoes available. The number of potatoes is determined by the number of potatoes which farmers grow. If no person is willing to grow potatoes, but everyone is a multi-millionaire, then there will be no potatoes to eat.
So.... if the record keeping (the economy) falls apart, the number of automobiles, houses, laptop computers, tomatoes, ears of corn, bathroom toilets, etc... remains unchanged.
If you want the standard of living to remain high you have to have most people working.
Will the economy collapse? Maybe yes a day maybe no. The real question is, will people continue to make goods and offer services? In the event of economic collapse, would taxi drivers still drive people to the airport? Would petroleum refinery workers keep working ? Would electricians put wires inside of halfway built houses? Would computer programmers continue to maintain Google email services?