In investigating the claim "Texas A&M tightens discourse about race and gender in classes." I found that the claim is true, since all the information correlates with primary sources (The Battalion), and secondary trust sources (The Texas Tribune).
The primary source is The Battalion is the Texas A&M student's newspaper. The article explains the main reason why the Board of Reagents have made more strict the discourse of race and gender. Recently, a student secretly recorded his argument with professor Melissa McCoul, and after the video being widely spread, the professor got fired.
Ever since then, the University have reduced this problem by implementing this new policy, that "no system academic course will advocate race or gender ideology, or topic of sexual orientation, unless the course and the relevant course materials are approved in advance by a member of CEO"
The secondary source is The Texas Tribune, which is an independent organization focused on informing politics and policies in Texas. This news explains the 10 testimonies of professors regarding this policy. Furthermore, this only makes the fact-check more truthful as it is still a hot topic nowadays.
In conclusion, I have confirmed by primary source is The Battalion and secondary source is The Texas Tribune, that the change of policy at the University of Texas A&M with the regard of restricting use of race and gender language is true.