TX has a very strong business lobby - they regarded forcing carry privileges anywhere as deterimental to their financial interests for liability. Thus, they would oppose school carry and/or guns in the parking lot.
They are 'conservatives' in the sense that they try to conserve their money. They care little about any civil rights that stand in the way of the profits or risk them.
They play the theoretical 'conservative' property rights issue in a totally hypocritical fashion.