Anyone, including religious people, can claim science is on their side. Anytime someone have strong feelings they run the risk of ignoring facts. People tend not to admit they are wrong, and once they commit strongly to something they will probably not back down.
Yes Yucca Mountain is supposed to be a long term storage facility for the nuclear waste generated in the US. Currently plants store the waste on site, and since there is not that much to begin with this isn't much of a problem. The whole thing could be better dealt with if we just reprocessed it.