I think the main thing is nr 4, denying past atrocities is quite bad and way more sensitivie and tense topic, but nr 4 is directly against the democratic foundation of the EU. That you can be prosecuted simply for questioning the demi-god status of Ataturk, or pose much of differing opinion. Turkey as a country has alot of potential, but things like this is something they have to overcome to grow as a country.
But yeah, even if it werent for those conditions, I pretty much doubt they would be allowed in simply because of their religion. There is way too much islamophobia/xeonophobia in Europe to say the least, to get a majority acceptance for them.