If we were to present a 19th century carpenter with a nail gun he would agree upon demonstration; "that is very nice and all, thanks but i'll stick to my hammer". He would have neither a compressor, gasoline and a long enough hose, nor a wall socket and extension chord. The nail gun has no place in his toolshed because he doesn't have the required infrastructure and context to put it to use, and therefore the utility of the nail gun to him is close to zero.
Beliefs are the same, and a relation to "facts" or "truth" is not a requrement for their utility. When presented with new facts and truths we always evaluate their utility before we ascribe to them. We might fool ourselves that this process is somehow "rational" but rationality is just a social preference with some second-order effects with regards to science and the developement of technology (which indeed has "utility" but is far from the only "utility" beliefs can achieve).