Do I have to pay self employment taxes if my Adjusted Gross Income comes out negative?

Yes.  Self-Employment taxes are separate from federal income taxes owed and are not based on your AGI but on your net self-employment income.

But as the religious employment is consider an uncommon situation, even if in turbotax I click on "pay self employment tax" the program puts zero automatically if the AGI is negative. Just wanted to make sure that is correct or if I have to override it. Thank you

If your self employment income is negative then you have no worries at all.

@SA70