If the road system in a gated community is maintained by local government (taxpayers) how can an outsider be refused entrance

This is a really good question. It is fact specific so I am going to use a local community as an example. Lock Rane Blvd. in Orange Park, Florida extends into a gated community known as Orange Park County Club. The road is a private road, owned by the Country Club of Orange Park Partnership. It has granted access easements to parcel owners within the club for access to the road, but it is a privately owned and maintained road. The property owners of the within the community pay for maintenance; the taxpayers of Clay County do not shoulder any expenses. It entered into an agreement with the county for traffic enforcement, but it is not a public road. I'm sure there are other privately owned roads that operate under this agreement. The owner of the road has the authority to exclude people from access. Great question, I hope this was helpful.

I agree with my colleague's response and would add that the roads you are talking about most likely are not being maintained using taxpayer funds, except those of the taxpayers who live in the community and who, through their HOA, pay for the roads. Since the roads and the community are private property, they can exclude anyone they like or place restrictions on entrance.