As far as animals go the Texas law says up near the top where it is saying what it covers that it:
> does not, except as expressly provided by this Act, affect the authority of a municipality to adopt, enforce, or maintain an ordinance or rule that relates to the control, care, management, welfare, or health and safety of animals;
so it at least gives the appearance that it isn't going to allow people to just do whatever they want with animals.
But then much farther down in the miscellaneous provisions section it says:
Sec. 229.901. AUTHORITY TO REGULATE ANIMAL BUSINESSES.
(a) A municipality may not adopt, enforce, or maintain an ordinance or rule that restricts, regulates, limits, or otherwise impedes a business involving the breeding, care, treatment, or sale of animals or animal products, including a veterinary practice, or the business ’s transactions if the person operating that business holds a license for the business that is issued by the federal government or a state.
(b) Except as provided by this subsection, a municipality may not adopt, enforce, or maintain an ordinance or rule that restricts, regulates, limits, or otherwise impedes the retail sale of dogs or cats. A municipality may enforce or maintain an ordinance or rule adopted before April 1, 2023, that restricts, regulates, limits, or otherwise impedes the retail sale of dogs or cats until the state adopts statewide regulation for the retail sale of dogs or cats, as applicable.