It is me whom she loves
It is I whom she loves
Because I know that "It is I" is grammatically correct.
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You would have to break this down into two separate clauses to understand which pronouns you should use.
"It is me" whom she loves can be broken down into two parts.
"Whom does she love?" "She loves me"
Remember what is doing your action because that will determine whether you use I or me.
"Me" does not do the action. "She" does it.
She does it to "whom" and she does it to "me"