Yes They Can..I worked for a well Known Car Parts Distribution company that wanted me to collect chemicals ( used gunwash) 25 litre drums that were not secure without lids in my van, an absolute disregard for my and others road users safety i refused and was dismissed ,and very happy to leave as health and safety is paramount in my opinion, not to my boss though.
He kept giving me a bad references after i left ,so i simply used my previous employers before this job and referees for my good Character references .You can soon get new references from your next jobs. Resigning would be better .Good Luck.