Yes, enclaves within closed borders can lead to violent clashes. The residents of these enclaves must often cross hostile territory in order to make it to the main landmass where their fellow citizens live. Because they are forced to do this, they are very susceptible to attacks by people in other factions.
It isn't always easy for different cultures to live in such close proximity, especially when the beliefs of two cultures don't always mesh well together. While many people will get along, there will always be those on the extremes who are unwilling to understand that others think a different way around the world, and this is when the violent clashes occur.
Enclaves are not what lead to clashes. The violent clashes are because of the long history of social and political problems that people in these regions have been involved in for hundreds of years. These problems are not easily solved and in fact may never be able to be truely resolved.
Territorial disputes are often related to the possession of natural resources such as rivers, fertile farmland, mineral or oil resources. However, these disputes can also be driven by culture, religion and ethnic nationalism. To say though that all enclaves within closed borders lead to violent clashes would be a foolish thing to say