Are all four gospels in the NT accepted by every Christian denomination (whether trinitarian or non-trinitarian)? For example, you could have a christian denomination that accepts Mark’s gospel but rejects the other gospels. I don’t know for sure. These are just speculations.
I can't find any evidence for whole denominations which reject any of the Gospels, however among scholars the most contestable book tends to be the book of John. In particular the authorship and age of the book of John is a controversial subject - and if you consider this to be an important factor in whether John is a genuine gospel, then this will affect whether or not you accept the book as inspired.
As I say though, this isn't really a denominational issue so much as a scholarly one.
There have been issues with some of the letters on the other hand - for instance Martin Luther originally had issue with the inclusion of Hebrews, James, Jude and Revelation. Also Syriac Christian traditions didn't initially accept 2 Peter, 2 John, 3 John, Jude and Revelation. Both of these traditions ultimately came to accept these though - the main difference remaining is over the Deuterocanonical books which are included by Catholic/Greek Orthodox traditions but only deemed "useful for reading" and removed from the Biblical Canon in the Protestant traditions.