Yes, TX recognizes your WA permit.
I can't comment much on the sign you saw without knowing exactly what it said. There have been reports of confusion regarding places that sell alcohol thinking they were supposed to ask to see permits, but it is NOT a requirement of the store to do so. The fault is in if they knowingly allow unlicensed carry. They have no reason to suspect that carriers are unlicensed.
That said, all carrying in Texas is by license, so yes, you do need your permission slip.