I defended last month, got my PhD and am about to run out of funding. I've been applying to postdocs for close to a year and have only had one near-hire (something happened with their funding) and three interviews. One thing I've heard from a few sources is that, at least in this field, graduate and postdoc research should line up very well. My advisor even said it would be "a waste of time" to apply to postdocs that don't line up with my research extremely closely. Is this true?

I know that in other fields, like bio-med, it's actually encouraged to do something totally different. It seems ineffecient to only hire close match-ups.