Oh yes, absolutely. There are many other great books for the national market by LDS authors that don't mention the Church, but are exciting, clean stories. Books by Gordon Ryan, for example. He's written some excellent political suspense novels among others. Check him out on Kindle for some 99 cent deals.
Other LDS authors include Rachel Ann Nunes, David Wolverton, Jennie Hansen, Orson Scott Card, Gerald Lund, Jack Weyland, G. G. Vandagriff, Annette Lyon, Josi Kilpack, Julie Wright, Tristi Pinkston, Jeff Savage, and many, many more.
If you go to
http://www.ldstorymakers.com you can find a long list of LDS authors who write in a variety of genres. And, of course, there are more who are not on this list. In my opinion, these days, the standard of writing from the majority of LDS authors is excellent.