Thank you for your question. I look forward to working with you to provide you the information you are seeking.
Under the NM and Federal laws, businesses open to the public have the right to allow in anyone they choose and can refuse to admit anyone they choose. The ONLY exception to this is that they cannot refuse to allow you in or serve you based SOLELY on your age/race/sex/disability/national origin/religion. Thus, in order to have a case to bring to the District Court or even possibly to the federal court, you must have evidence that you have been denied service for one of those reasons above I mentioned.
Unfortunately, absent evidence that you were refused service based on age/race/sex/disability/national origin/religion, the lower court was correctly stating to you what the law in NM and the federal laws state and I am afraid that the District Court would be bound by those same laws. Even though you feel you have been unlawfully refused, you have not mentioned any of the reasons that I mentioned above that would make they refusal to serve you unlawful. Unless you have evidence of one of those unlawful reasons, any business open to the public can refuse to serve or even admit onto the premises anyone they choose for any other reason or no reason at all and that is what the law says I am sorry to say because these businesses are private businesses even though they are open to the public.
If the buildings are government buildings then your argument is correct in that they cannot make you leave a government building or refuse to serve you in a government building without good cause because those are not private businesses.
I truly aim to please you as a customer, but please keep in mind that I do not know what you already know or don't know, or with what you need help, unless you tell me. Please consider that I am answering the question or question that is posed in your posting based upon my reading of your post and sometimes misunderstandings can occur. If I did not answer the question you thought you were asking, please respond with the specific question you wanted answered.
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Also remember, sometimes the law does not support what we want it to support, but that is not the fault of the person answering the question, so please be courteous.
This is NOT the practice of law nor is it legal advice to you, it is merely educational information for you to use to seek out a licensed attorney in your state to get actual legal advice from them. Please use sites such as http://www.martindale.com or http://www.lexmundi.com or http://www.hg.org to find a local attorney to get actual legal advice in all matters.