Is it obligatory to commit to fulfilling what is asked of you if someone says "By God, I implore you" and repeats their oath for trivial matters or for actions that you do not deem righteous to perform?

Fulfilling an oath is commendable, based on the hadith of Al-Bara' ibn 'Azib, may Allah be pleased with him: "The Messenger of Allah, peace and blessings be upon him, commanded us with seven things... and to fulfill an oath."

The majority of scholars interpreted the command to fulfill an oath as a recommendation (nadb), not an obligation. Evidence for its non-obligatory nature is that the Prophet, peace and blessings be upon him, did not fulfill the oath of Abu Bakr Al-Siddiq, may Allah be pleased with him, when Abu Bakr swore to him that he would inform him of the error in the interpretation of a dream.

The command to fulfill an oath applies when there is no corruption (mafsadah) or apparent hardship (mashaqqah) in fulfilling it.

As for someone who asks by the Face of Allah, there is a prohibition against refusing them if they ask by it, unless they ask for something to be abandoned. It is commendable not to ask by the Face of Allah for anything other than Paradise.