This became such a thing that the Paso Del Norte Tejano Democrats Chairman Eddie Holguin reached out to the State Chairman to ask him if that was the case.
In his emailed response, Chairman Hinojosa very clearly states, "Eddie, the Texas Democratic Party never encourages Democratic voters to vote for Republicans - and never will."
Later Chairman Hinojosa also states, "If voters want to go to the polls and vote on any of the other contested elections on the ballot they should be encouraged to do so. If they don't want to vote for any of the mayoral candidates then they should skip that position on the ballot or vote a write-in name."
So for those of you in the Party that are being told that the TDP doesn't want you to undervote, here is clarification from the Chairman of the Party himself.