There is no such sharp division atm. The alliance against RTE includes the neo-Ottomanist Davutoğlu(AKP's former chief advisor, then foreign and prime minister), the Atlanticist Islamist Babacan (AKP's former EU negotiator, then foreign and economic minister) and the direct political Islamist Karamollaoğlu. Among the parliamentary candidates are people who were ministers of justice and senior security bureaucrats during the Balyoz and Ergenekon conspiracy trials organised by the US-controlled Islamist terrorist organisation FETÖ. One of the chief writers of FETO's unofficial publication and daily newspaper is one of KK's chief advisors today and was made a candidate for Izmir 1st place deputy as if making fun of secularists from Izmir.
Ulusalcılar (white Turks, as you call them) have been largely eliminated from the CHP, and former CHP member İnce is seeking their votes with his candidacy. At the moment, CHP media and troll armies are primarily targeting İnce, not RTE. An incredible lynching campaign is underway. The 4th candidate, on the other hand, aspires to get the votes of the more Turkist and right-wing nationalist secularists. However, he cannot gather enough strength due to the two major nationalist parties in both the ruling and main opposition wings. Even the AKP has started to include figures who have been recognised for years as Atatürkist secularists within the party. Moreover, In the mainstream media, RTE's biggest defenders are secularists like Nedim Şener, who is on FETO's death list.
So the situation is much more complicated than you think. But if I have to make a classification, I prefer to divide it into two as neo-eurasianists tendency and Atlanticist tendency. As a matter of fact, in an interview with a major news organisation, former Prime Minister Davutoğlu blamed the Eurasianists for the his *** kicked from Akp and all its cadres being purged. In his own words, 'they purged us and Eurasianists took our place'.