1. It was you (that) told me to say so.
2. It was me (that) you told to say so.
Can 'that' in these sentences be omitted?
We can only omit "that" before a relative clause if it is not the subject of that clause. In #1, "that" is the subject of "that told me to say so"; it cannot be omitted. It is optional in #2.
Pope of the Dictionary.com Forum
I would use "who", not "that" anyway.
It was you who told me to say so.
It was I who told you to say so.
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