That's exactly what I was doing tonight ... I use foam core, and use push pins to hold the blocks in place. And yes, out fairs say you must use safety pins only. However, there's never been a problem. I like the foam core, as when they display the block, it keeps it all sitting nice and perky, whereas bristol board can flop so easy.
Tartan has a good suggestion ... however, when Judging I would suspect they will want to look at the back. Having them stitched in place would not be conducive for that. At least that has been my experience when showing blocks.