Jonathan Joss ' husband Tristan Kern de Gonzales is convinced he was gunned down in cold blood by a neighbor due to homophobia -- but cops are pumping the brakes, saying they’re not calling it a hate crime just yet.

The actor -- best known as the voice of John Redcorn on "King of the Hill" -- was shot dead on his own property Sunday evening -- and cops are saying that right now there's not enough proof to back up Tristan's claim it was a hate-fueled attack.

San Antonio Police posted an update on X Monday, writing, "Despite online claims of this being a hate crime, currently the investigation has found no evidence to indicate that Mr. Joss’s murder was related to his sexual orientation."

That’s a direct hit against Tristan’s viral post -- where he flat-out accused their neighbor of be

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