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?
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.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.