Can Police refuse to enforce a court order because they say it is a civil matter?

Yes they can, however, this depends on the nature of the court order. If the court order is a civil judgement (small claims lawsuit) then yes this is a civil matter. However, if the order specifies something to the nature of: Police shall provide security the named plaintiff, when she/he on such and such dates, arrives at such and such place to remove such and such property. Then no, the Police cannot refuse to enforce the order since doing so would violate the order.

Child Support and Civil Debts, are civil matters and outside the jurisdiction of Law Enforcement. Where as if the Police are listed in an order or this is a court ordered custody exchange and a parent kidnaps a child beforehand, or an order for safety or protection then the Police are required to enforce it.