: Fundamentalism is not only the enemy of feminism in Turkey,

It isn't. It's largely irrelevant to it. The regulation of women is not one of its major concerns.

: but a huge roadblock for progress in the US.

You have a very different situation there.

: Knowing that, one can only speculate what a huge catastrophe it would be for Turkey
: to come into the EU.

The forces within Turkey that don't want entry to the EU are precisely the nationalist-fundamentalist axis. The people behind the Kurdish war and the hardline on Armenian genocide denial (e.g. the judicial harassment of Orhan Pamuk) are precisely the political class put into positions of influence by NATO in the 1980s. Keeping Turkey out of the EU is sending them the strongest message of approval they could get from the West.

I was in Hasankeyf a while back - a historically important Kurdish town threatened with obliteration by a British-bankrolled dam project. The Turkish government was only too delighted to use electricity generation as an excuse to wipe out an icon of Kurdish culture. The EU stepped in and got the project stopped. The locals are the most pro-European folks you could hope to meet outside of a cafe in Strasbourg. (The Turkish government and British banks have now threatened to restart the scheme).