What is the ruling on praying behind an Imam whose transitional takbirat do not coincide with the transition (before bowing for ruku' and after the forehead touches the ground in sujud)? And is praying behind him more preferable than praying behind someone who shaves his beard?

The prayer behind the mentioned Imam is valid, and it is better than praying behind someone who insists on shaving his beard, because insisting on shaving it is considered a sin (fisq) unless he is following an opinion that deems it merely disliked (makruh (definition)), and he deserves to be disciplined. As for the transitional takbirat, the prescribed way is for them to coincide with the movement, but they are not among the obligatory parts of the prayer; rather, they are a recommended sunnah (definition). If the Imam omits them, his prayer and the prayer of those behind him are still valid.