I could be talking rubbish here, but it seems to me that evangelicals are fundamentally Platonists in their view of the Church, while catholics are Aristotelian.
(OK, I’m generalising a bit here!)
Evangelicals broadly think the fundamental ecclesiological relationship is between the believer and the invisible Church. The idea of the church, the Body of Christ, existing beyond time and space, is the real church. These believers can and should get together in fellowship with one another, and some of those fellowships are called churches, but the organisation and ministry of those churches is at best a secondary question and quite often a matter of indifference.
Catholics on the other hand essentially think that the only way you can really conceive of an invisible church, and certainly belong to it, is to have an actual physical assembly with a structure and physical practices of belonging. The organisation of the church is a primary matter of faith because it’s impossible to conceive of Jesus’s invisible community in eternity, without reference to the community he founded in history.
I think that’s still one of the main reasons for incomprehension within the Church of England, and more widely between different Christians and their ecclesial bodies.