These people would leave turkey if possible, but they can't.
This is making turkey less western?
Wouldn't that have the opposite effect? The west is generally responsible for the brain drain in less successful countries. Throwing borders up will keep those people who share our views in those countries. It's a fair bet that those people will be the force for good change in their governments more likely within their country than outside it.
Could it be an example of a tragedy of the commons?
No one wants to drink water where someone shit but everyone would rather shit in the water than in a field somewhere far and away from the ability to clean oneself.