I've been using freezer paper, but it's such a chore to cut every time, and if I don't get the corners covered, I get leakage and ugly soap. So last batch, I used a cheap, very flexible cutting board to make permanent liners for the ends. I get them at Ocean State Job Lot (cheap odd lot store in the NE) for about $1.50 a pair. I cut it a little larger on all dimensions than the ends, then used a razor knife to lightly score to fit inside, then bent the edges out. I cut the corners slightly so that they overlap. then I used freezer paper along the long edges, and it all worked quite well. I did only the ends because I had pieces left from other projects (they make great stencils for quilting) and didn't have enough to do the center as well.
The only difficulty so far is that, since I made my molds, they're not exactly the same sizes, so each liner set had to be customized and marked as to which end, which mold.