I read contemporary books out of duty all the time because I belong to a book club where the members each take turns deciding which book to read each month. So, in the past decade, I've had to read books by Jody Picoult, Anne Perry, Anita Shreve, Isabelle Allende, Maeve Binchy, Barbara Kingsolver, Anne Tyler. I find most of them too trendy for my taste, but I read them as a loyal member of the book club.
But I was also introduced to some contemporary authors whom I now love: Carol Shields, Elizabeth McCracken (her short stories), and Jamie O'Neill (the lone male among our authors, he wrote "At Swim, Two Boys"), among others.
My own choices for book group tend to be classics, particularly the Russian authors and Jane Austen. I've also chosen books by Willa Cather and Rumer Godden for our group to read. In the book group through the years, I know that certain members won't read any book I suggest except for the first few cursory pages, and I often do the same with one member's choices.

We're all OK with that, however; although we start off sticking to the book, our conversations always manage to veer off about halfway through our session into topics that require no reading of the book.
I'm glad to have had the exposure to these novelists despite my being a rather persnickety reader. It took me years to leave the classics domain and explore contemporary works.