For me (and I'm NOT a lawyer), the operative word in the quoted law would be "stored".
A gun on your person is not "stored". therefore, requirements for locked storage cannot apply. But, that's just me...
Adoption agencies can require what ever they want, over and above existing laws. They aren't looking at you simply for compliance with the laws, they are looking at you to see if you meet their standards, which, as you have seen are much different from actual law.
There is nothing in law about how much money you have to make, or how clean your house has to be, etc., but there is in their standards.
Adoption is a privilege, not a right. The only place the law enters into it is the fact that the law gives them (the agency) the authority to make the decision.
I have no idea if there is a "surplus" or a "shortage" of people wanting to adopt, either way, I don't see them changing their rules. They might bemoan the lack of "suitable" or "qualified" parents, based on their standards, but they are very unlikely to change their standards so more children might be adopted. If they don't approve you, the child just stays in foster care, and to their mind, is no worse off than before.
Essentially it seems to me that your argument is "I comply with the laws, that should be good enough", and theirs is "You must meet our standards (which are "tougher" than the law) or we won't give you one of our children". And, apparently they have the legal authority to do so.
To over rule their decisions, you would have to win in court. Good Luck with that.