There will likely be as many different answers to your question as there are denominations.
From an Evangelical perspective, I'd venture a guess that ecumenism is a "hard sell" in many Evangelical denominations of whatever stripe. (I would not even dare to give you a list of Evangelical denominations!) I happen to be a member of the Christian and Missionary Alliance (C & MA) Denomination, a worldwide movement which is obviously “missions minded”! The denomination was founded by a Canadian preacher, theologian, and author, A. B. Simpson (1848 – 1919).
Thirty years after the founder of the C & MA went to be with his Lord, an ecumenical organization called the "The World Council of Churches" (WCC) made some headway in the 1950s (and beyond) in uniting some denominations, particularly the more "liberal" churches. These churches, by and large, emphasized the "social gospel" and de-emphasized "the gospel, period"!
Back then (in the 1950s), believers in "the gospel, period" would not say their gospel was a "holistic gospel," but in retrospect that's really what it was. To these folks, the gospel of Jesus Christ addressed the whole person: spirit, soul, and body. They considered the "social gospel" a truncated gospel, and from an Evangelical perspective they were right.
From their perspective the "liberal, social-gospel types" overemphasized the social aspects of the gospel and deemphasized what to them was the all-important spiritual aspect of the gospel, particularly the new birth which Jesus taught (John 3:1 ff.). Generally speaking, then, the "gospel, period" folks were correct. The WCC, well-meaning though it may have been, did tend to emphasize what might fairly be called "justice issues" but shied away from the kerygma of the first-century church. You might say the WCC didn't want to seem preachy, and in James-like fashion came down on the side of works, rather than grace. (James, I realize, was not an "either/or man" regarding faith and works; he was, rather, a "both/and man" who wedded faith and works in, well, a holistic package. Here is James’s “take” on faith and works:
Even so faith, if it has no works, is dead, being by itself. But someone may well say, "You have faith and I have works; show me your faith without the works, and I will show you my faith by my works" (James 2:17-18 NASB Updated, my italics).
Interestingly, according to Wikipedia, the Roman Catholic Church took a less-than-active role in the efforts of the WCC. Representatives of the RCC would attend meetings only as observers, not as participants.
Reformation 21, an evangelical parachurch ministry with roots in the Christian Reformed Faith, published an article recently titled “Encouraging Sign of Ecumenism in the 21st Century, “ by Mark McDowell (March 2015). Here are a couple paragraphs from that article:
Twenty-one years ago to the month [i.e., March 1 1994], a group of ecumenically-minded Evangelicals and Roman Catholics, led by Richard John Neuhaus and Chuck Colson, gathered together and issued the statement: 'Evangelicals and Catholics Together: The Christian Mission in the Third Millennium (ECT)'. It first appeared in New York on Tuesday, March 29th, 1994 and a few months later was published in First Things. While many applauded and welcomed the document at its launch, it was also met with intense controversy and a great deal of suspicion. To this day some would argue that not much has changed.
ECT was crafted with the purpose of finding some agreement on the core tenets of Christian teaching. From this standpoint, it urges Evangelicals and Protestants to act together, as far as 'divergent convictions allow' (JI Packer), on matters of cultural and moral concern. 'Co-belligerence' at the grassroots level is at the heart of ECT's mission, prodding both communities to collaborate together against the corrosive effects of Western secularism. One of the recent products of its labours is the statement on marriage found in the recent edition of First Things.
For many years there has been a natural antipathy between Evangelicals and Roman Catholics. The primary “sticking point” seems to have been the differing perspectives on the role the Scriptures should play in the life of their respective churches. Ever since Reformation times, an era in which Protestants objected to certain excesses of the RCC (e.g., indulgences), the “mantra” of many Protestants regarding ultimate authority has been “Sola Scriptura” (Scripture only). On the other hand, a radically divergent mantra for the RCC regarding ultimate authority (for which I have a neologism) has been “Sola Ecclesia.” (Church only). (I apologize for my conflation of Latin and Greek!)
While I am not speaking for my denomination, I surmise that the “ultimate authority issue” is a big pill for both Evangelicals and Roman Catholics to swallow. I would like to think that in matters which are important to both camps (e.g., missions and a kerygma-based evangelism), we could somehow and in some way simply agree to disagree agreeably regarding ultimate authority and forge ahead with tasks we both can be wholly committed to. That, however, may be wishful thinking on my part. To this day, many Protestant denominations (not my C & MA, I’m glad to say) are convinced the RCC will figure prominently in the Apocalypse, and not on the side of the good guys! And I’ll leave it at that!