I've read mixed opinions of Thomas Merton and Dorothy Day by various members of St. Blog's parish, and they are indeed the most controversial of the American Catholic writers portrayed in Elie's book (the other two being Walker Percy and Flannery O'Connor).
Merton's spiritual autobiography Seven Storey Mountain was well-recieved not only by the American public but readers around the world, through which he acquired a kind of 'celebrity status' as one of the most popular Catholic personalities in the twentieth century. However, his counter-cultural participation in the peace movement, sharp criticism of the U.S. during the Vietnam and Cold War tarnished his reputation in the eyes of those readers who percieved him as a traditional Catholic.
Likewise, Merton's appreciation and engagement with Hinduism, Buddhism and Sufism in the later years of his life -- anticipating, I believe, the interreligious dialogue proposed by Vatican II's Nostra Aetate -- was heavily criticized and portrayed by some as an abandonment of his Catholic faith.
There are many sides to Merton, as evidenced by the recollections of several close friends and discussed in Robert Royal's essay The Several-Storied Thomas Merton (First Things January 1997, pp. 34-38), and despite such criticism I find myself agreeing with Royal's assessment that:
Merton's true greatness lies in having engaged in person the whole range of challenges and trials of life in the late twentieth century and yet remaining essentially faithful to his Catholic inspiration. . . . His personal turmoil and the misjudgments in his social thought notwithstanding, he is a forceful reminder that what may appear the most rarefied of contemplative speculations have powerful and concrete implications for the world. God dealt Thomas Merton a difficult hand. His greatness as a man lies not only in that he was able, more or less, to keep several different persons together in difficult times under the banner of "Thomas Merton," but that he provides an enduring witness to all of us much less gifted seekers who have to shore up our own fragmentary lives in quest for the "hidden wholeness."
There is not a great deal in Dorothy Day's religious thought and behavior that would invite criticism from traditional Catholic critics. According to Jim Forest:
Whether traveling or home, it was a rare day when Dorothy didn’t go to Mass, while on Saturday evenings she went to confession. Sacramental life was the rockbed of her existence. She never obliged anyone to follow her example, but God knows she gave an example. When I think of her, the first image that comes to mind is Dorothy on her knees praying before the Blessed Sacrament either in the chapel at the farm or in one of several urban parish churches near the Catholic Worker. One day, looking into the Bible and Missal she had left behind when summoned for a phone call, I found long lists of people, living and dead, whom she prayed for daily.
However, like Merton, Dorothy Day was a prominent critic of modern culture, and her unwavering solidarity with and service to the poor, unflinching pacifism, and vehement criticism of Western capitalist consumerism placed her at odds with many in society, especially the economically-advantaged.
Sadly enough, while some may have legitimate differences with Dorothy's politics, there are also critics who like to dredge up Dorothy's past, including the fact that she was a divorcee (from a "common-law" marriage) and had an abortion in her bohemian days. While they see this as grounds for opposition, I find it all the more reason to celebrate her life as a testimony to God's abundant grace and forgiveness. Perhaps they ought to listen to Cardinal O'Connor, who recognized that it was Dorothy's very opposition to abortion that made her an appropriate model for our time, and advanced the cause for her Beatification and Canonization in 1997.
I encountered the writings of both Thomas Merton and Dorothy Day as a junior in college, then a lapsed Christian engaged in intellectual flirtation with existentialism, radical politics and Eastern religion. Zen & the Birds of Appetite was the first book of Merton's I ever read, and provided me with an impressive incredible example of how a Christian can engage in interfaith dialogue with clarity and wisdom. Shortly thereafter, curiousity aroused by conversations with a Catholic Worker friend, I read Dorothy Day's spiritual autobiography The Long Loneliness, and as one questioning whether religious faith and political commitment were in irrevocable conflict (aka. Marx), Dorothy provided a worthy example of how to integrate the two.
I can honestly say that without the spiritual influence of both writers, I probably wouldn't be writing this blog today, and for that I'd heartily second Amy Welborn's recommendation.