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When at the appraisal district, it being public/government property, one might be correct in assuming it's no one's business regarding who has a license or not. OTOH, the above interaction sounds like it was conducted respectfully and I'd have no problem showing my license.

In Walmart, Sam's, or any other private property place, where they have the authority to tell you not to carry, it's probably appropriate to confirm that you have a license and show it when asked. This would be particularly true in an establishment that sells alcohol, since the business is subject to a fine if they allow anyone who is not licensed to carry a weapon inside their premises. I look on it as they're simply doing their due diligence by confirming that you're not carrying illegally.

Other folks may have other opinions, these are mine.