Global warming is a theory accepted by a majority of scientists. How can local environmental changes have global effects?

The local environmental changes are having a global effect, and that is well documented and constantly witnessed. The reason why local environmental changes can have such a big impact is that the gasses move freely throughout all of the planet, they move horizontally with the winds, and they also move vertically higher into the atmosphere which is in constant movement.

This results in a situation where one area produces lot of pollution, but another area is feeling the effects because the air masses moved big portion of the polluters there.

A nice example are China and Mongolia. China is one of the two major polluters in the world, while Mongolia barely has any industry especially when considered its size and population. The air masses though are moving from the southeast towards northwest, thus big portion of the pollution in the eastern part of China goes into Mongolia. Because of this, despite not being a big polluter, Mongolia has one of the worst air qualities in the world.

Also, we can witness that the holes in the ozone layer are mostly around the poles, despite the sources of the chemicals that are damaging it are on totaly different locations.