I would presume that this is legal (without researching the laws in Cali. or Texas).
Their contract is an offer to enter into an agreement. You accept that offer by signing. Their pre-requisite for that offer is that you pay the nonrefundable application fee. In other words, they are refusing to make you an offer until you pay a set fee.
Now the degree of negotiability, among other factors, would go into determining whether the contract is fully enforceable.
I did a little bit of research. (Please note that this is not legal advice. If this applies to a current situation, seek the advice of an attorney licensed to practice in your jurisdiction.)
There does not seem to be any indication that the landlord needs to provide a sample lease to you before s/he decides that you are an eligible applicant. The application fee is not a contract to rent the premises; it is an application to be considered a tenant.
Pro-Business Perspective: Why would I (the landlord) waste my time going over an application with someone and show them a model unit if they are not even eligible to rent from me? I have better things to do.
Pro-Consumer Perspective: Why waste my time and money if I refuse non-negotiable terms in a lease?
The application fee is capped in California and must be used to cover screening costs or refunded if not used.
The likelihood of success in a claim regarding this might be indicated by the California Dept. of Consumer Affairs: "If you don't like the landlord's policy on application screening fees, you may want to look for another rental unit. If you decide to pay the application screening fee, any agreement regarding a refund should be in writing."
It is important to note that you can always try to negotiate with the landlord. Personally, every lease I have had I have negotiated to get more favorable terms. You, as a tenant, have every right to try to negotiate, and should use that right.