What is the ruling on praying behind the mosque’s imam when some of the worshippers dislike him, knowing that he is the mosque’s preacher but he misses Fajr prayer once or twice a week?

If the questioner does not clarify the reason for the congregants' dislike of their Imam, then the prayer of the congregants is valid, whether their dislike is justified or not, as long as the Imam does not do anything that invalidates the prayer. The dislike pertains to the Imam and does not affect the validity of the congregants' prayer. The Ahadith that convey a warning to one who leads a people in prayer while they dislike him are directed solely at the Imam, and his error falls upon him, not upon the congregants.