The Republicans say that "homosexuality must not be presented as an acceptable alternative lifestyle, in public policy, nor should family be redefined to include homosexual couples." Therefore, it wants to take away their right to marriage by overturning the U.S. Supreme Court case that granted it nationwide, and wants to make sure that anyone in Texas who seeks to discriminate against gay people won't face any consequences. The platform also seeks to ensure there are no restrictions on "counseling and therapy" to designed to "change" someone's sexual orientation.
As for transgender people, you guessed it: Texas Republicans want to police bathrooms by preventing transgender people from using the restroom that best fits their gender identity, which is generally affirmed by a court of law. Republican leadership is so committed to this goal, in fact, that Lieutenant Governor Dan Patrick said he would be willing to flush more than $3 billion in federal education funding down the toilet just so he could ignore President Barack Obama's directive to school districts not to discriminate against transgender students by denying them access to the right bathroom.
Support for discrimination doesn't end with the LGBTQ community. In order to defeat terrorism, the Republican Party would like to support the "reasonable use of profiling," though "reasonable" is never defined. It would also like to call on all government agencies to sever ties with "all radical Islamic organizations, such as the Council on American Islamic Relations."