Something that may not be clear on this thread yet is that ecclesiastical separation is not about individuals fellowshipping and being friends, no matter what their theology. I could easily fellowship with you on an individual basis, and I am sure I would profit from the friendship. My best friend for decades is a 5 point Calvinist.
Ecclesiastical separation is about churches cooperating in God's work. One important passage for this doctrine is 2 Cor. 6:14-18, esp. v. 14: "Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?" A yoke is where two animals work together. Therefore, Paul was telling the Corinthian church not to work together in God's work with those who are not true believers. (In my book, that starts with Catholic churches, theologically liberal churches and other aberrant ministries.)
Wouldn't it be based though upon IF the church is teaching the Gospel and jesus, the biblcal versions of each?
If you were (are?) the pastor of a church and wished our churches to cooperate in an endeavor, at that time I would sit down with you (over Starbucks maybe) and discuss whether we were agreed enough to walk together in the effort (Amos 3:3).