Is it theoretically possible for enough food to be produced on each continent to the point that intercontinental shipping of it could end?

Not likely. There are too many overpopulated countries that don't have the farmland to provide enough for their citizens. Ethiopia, Somalia and Djibouti come to mind. Also, America's ravenous appetite for beef, exotic foods not produced here and out of season produce cause us to import much of it from Central and South America and Asia. There are other more complex, political reasons I am sure.

I have read that it's possible if we give up meat. The animals take up tons of space and then we need cropland to feed them on top of it. I don't know the details though.

Yes and No
     This earth is pregnant
with life food across the Earth.
     But there  are places where certain
types of food flourish in certain climates.
Because we enjoy varieties from around
the world, it's like there was a design to have 
different parts around the world to come together.
That the whole world be a big Family sharing in the  
fruits of the Earth.
     I love a Guava from India. To me that 
fruit is Moksha. For me to enjoy a Mango from 
India That intercontinental shipping is necessary.
We come together and share the world with everyone
through our food. This helps us in understanding
all peoples communicating in what is good for us.
An evolving understanding. 

it can be possible but not for every countries. very small ones cant do it .

also the thing is there will always be trade of foods because they want things that cant grow in their own

It might be possible in some countries but by no means all, and then only by accepting more limited diets and ignoring the self-appointed Diet Police.

It  may work in countries like Britain and Ireland, and a good many others,  thanks to good farming practices on a good balance of grass-land for dairy and meat animals to graze, other land suitable for cereal crops, large areas good for vegetable growing, orchards, etc.; and all under a temperate maritime climate (though of course, its future subject to whatever climate change will bring). 

Even then, with a population of >65M and growing, and many people growing food at home, we'd have to eat less overall without starving or malnutrition; and we could not have many fruits without importing them.  

In theory a continent the size of the USA or Russia ought be self-sufficient by sheer size, latitude range and variety of soils and climates; though continents can also suffer from wide extremes of climate. (Large areas of Siberia have the largest annual temperature range of anywhere.)