Your states Preamble - Page 2

You're leaving out a good bit of that part of the Texas Constitution of 1845 deals with religion:

SEC. 3. No religious test shall ever be required as qualification to any office or public trust in this State.

SEC. 4. All men have a natural and indefeasible right to worship God according to the dictates of their own consciences; no man shall be compelled to attend, erect, or support any place of worship, or to maintain any ministry against his consent; no human authority ought, in any case whatever, to control or interfere with the rights of conscience in matters of religion; and no preference shall ever be given by law to any religious societies or mode of worship; but it shall be the duty of the legislature to pass such laws as may be necessary to protect every religious denomination in the peaceable enjoyment of their own mode of public worship.

Despite their invocation of God, they didn't want the government tangled up with religion, either.

And just a side note, the Constitution of 1845 was repealed in 1861. So you're posting about a document that hasn't been the law in over 151 years. We've had four separate Constitutions since that one of 1845. That being said, the current Constitution, adopted in 1876, contains similar, if less florid language. The current Constitution also includes these provisions:

SEC. 6. All men have a natural and indefeasible right to worship Almighty God according to the dictates of their own consciences. No man shall be compelled to attend, erect or support any place of worship, or to maintain any ministry against his consent. No human authority ought, in any case whatever, to control or interfere with the rights of conscience in matters of religion, and no preference shall ever be given by law to any religious society or mode of worship. But it shall be the duty of the Legislature to pass such laws as may be necessary to protect equally every religious denomination in the peaceable enjoyment of its own mode of worship.

SEC. 7. No money shall be appropriated or drawn from the treasury for the benefit of any sect, or religious society, theological or religious seminary; nor shall property belonging to the State be appropriated for any such purposes.