Please be advised that I am licensed in California, not Texas; but in any case, lawyers in this forum cannot give specific legal advice for specific legal problems because no lawyer-client relation exists. But we can address generally aspects of the legal issued raised.
Now, at the risk of sounding like a lawyer, I'm afraid I don't have a short answer for you, and the answer probably is: "It depends.".
Off hand, I think this forceable sign issue may present a novel question of law.
As you know, sex offender registration has long been upheld as constitutional. And Congress has established minimum standards for such registries with the enactment of the federal Sex Offender Registration and Notification Act in 2006.
Not only have courts upheld sex offender registration as consitutional under due process and privacy protections, but also constitutional with respect to the First Amendment.
Just last year in UNITED STATES v. ARNOLD , the Fifth Circuit Court of Appeals established that laws requiring sex offender registration were not "compelled speech," rather found that such laws allow the government "to protect the public" and so "conducts an 'essential operation of [the] government,' just as it does when it requires individuals to disclose information for tax collection."
However, your scenario presents a different facet: Given that sex offender registries do not amount to compelled speech or otherwise violate the First Amendment, nevertheless can registered sex offenders be compelled to post signs on their own private property (or private residence) as to their registered status?"
It well established that government cannot compel speech (Wooley v. Maynard, 430 U.S. 705), but the Arnold case distinguishes compelled government-mandated ideological or political speech from that necessary to the "essential operation of [the] government" elucidated in Arnold, including such "speech" as sex offender registries, income disclosures to the IRS and even court testimony (that which is not protected by 5th Amendment).
So the constutionality of this sign issue is likely to turn on a determination as to whether the signs are "essential" to the operation of government and public safety, as a requirement IN ADDITION TO the state law requirement of registration.
As a matter of prognostication, I would say a challenge to a municipal ordinance requiring sex offenders to posts signs on their private residence regarding their registrations could succeed on the basis of violating the First Amendment. I think there would also be a privacy violation argument in this "sign scenario," even though privacy arguments have not been received favorable in past sex offender registry cases.
But if sex offenders can be required to post signs on private residences of this legitimate public information, can government also compel those who filed for bankruptcy to post signs at residence or business? Or require such posting from others convicted of other crimes as well? That seems unlikely.
Also, I think this scenario presents an argument that compelling those signs violates constitutional equal protection as well.
I hope this provides some perspective: i fyou find it useful, I would appreciate a favorable rating -- thanks!