What is the ruling regarding an Imam who denies the eternal damnation of Jews and Christians in Hell, and stipulates that a Prophetic Hadith must be logical in order to be accepted?

The imam is ignorant that "those who have earned Allah's wrath" are the Jews, and "those who went astray" are the Christians. This is something that should not be unknown to anyone who reads the Quran. Allah has explicitly declared the Jews and Christians disbelievers in clear verses, due to their associating partners with Allah, their denial of Prophet Muhammad (peace be upon him), and their rejection of his message, which makes them inhabitants of the Hellfire.

The scholars have unanimously agreed upon the disbelief of Jews and Christians, and even the disbelief of anyone who doubts their disbelief.

As for the imam's statement that he would reject a hadith if it contradicts logic, this is false. The "logic" he speaks of is the logic of disbelievers, which permits perversion, usury, alcohol, and other forbidden things. Such an imam is not a Muslim in the first place, and it is not permissible to pray behind him. It is obligatory to search for an imam with sound عقيدة (creed).