You can specify if you allow pets, past evictions, BK, etc.  

Straight to the point, is it legal in the state of Texas for an apartment complex to charge a pet deposit and to charge a monthly pet fee on top of that?

Might look good on paper but be prepared for evictions, stolen copper, stolen wire, stolen AC units, graffiti, smoking, illegal roomers and pets.

I have already warned them about violating the pet policy.

Think of all the things that could go wrong and see if the lease addresses them: unauthorized pets or tenants, early termination, security deposit, lease violations, late rent, eviction, lawn maintenance, parking, etc.5.

I have a no pets policy.

I could charge a per pet fee to add to my bottom line per month and collect a pet deposit upfront incase of damages. 

"90 gallon aquarium"$200 pet deposit*......

Co-living spaces, communal workspaces, rooftop gardens, fitness centers, and pet-friendly facilities are increasingly popular among Millennial renters and homeowners seeking a sense of belonging and community engagement.Impact of Demographic Diversity and Inclusion: Millennials are the most diverse generation in U.S. history, with a significant portion identifying as racial or ethnic minorities.

90% of the "ESA" pets are bogus and ruin everything for the real one.You cant straight up decline due to the ESA aspect...lawsuit waiting to happen.