This is state government in the role of "big government" overruling the wishes of local town or city small government.
No, you're absolutely incorrect. You seem to think that objections to "big government" are a simple matter of hierarchy and a desire to avoid upper tiers of a hierarchy from acting. But nothing could be further from the truth.
The federal government has a role. State governments have a role. Local governments have a role. Setting and enforcing immigration policy is the role of the federal government. When the federal government exercises that role, there is no "big government" issue at work.
The matter set here is a state government action, and one that is 100% within a state's discretion. Therefore, there is no "big government" issue here.