Now you may be like, "Norm, how do you know what good authentic tex-mex is supposed to taste like?" Let's see. I lived in Texas for 23 years. I am from Mexican american descent. Therefore I know Tex-Mex. Why? Because it's who I am. My grandmother cooks it in her kitchen every day for crying out loud.
Its funny that churches sometimes try to strategically "can" authenticity. Here's the deal, if you are a christ follower then be a Christ follower. Don't "act" Christian or try to convince people that you are authentic, that is not what God sent Christ for.
Colossians 3:3 says "For you died, and your life is now hidden with Christ in God."
If it's really Tex-Mex, you don't have to pretend, people will know. So if you (or your church) really are a caring, loving, passionate, selfless (etc.) Christ follower, people will know. So don't can it.