You can omit it in 2, as you can in "It was you I told to say so."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?
...and I wouldn't, but I'd promote the person told (I was tempted to say 'tellee' but resisted ;-)) to make it the first word, using a dummy 'the one/person... etc': 'You were the one I told...'/'I was the one who told you...'/'I'm the one you should...'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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