Uncle Matthew is a Patriot, which, in the context of the story, is someone who believes that the Puritan settlers have a right to rebel against the British Crown should the king attempt to remove their charter. Though Patriots are outwardly loyal to the King, their loyalty has limits, and if the king doesn't respect the settlers' laws and rights, then he'll find out exactly what those limits are.
However, Uncle Matthew's political stance doesn't always feed into his normal, everyday behavior. So, for instance, when William Ashby, the son of a self-proclaimed "king's man," expresses a wish to come and pay court to Kit, Matthew's makes the decision—without asking Kit, of course—that permission will be given to the young man to woo his niece.
On the face of it, this seems like a strange decision for a self-confessed Patriot to take. After all, if William and Kit develop feelings for each other, then they may well be married one day. Then we'd have the strange situation of two families with radically different political opinions being related by marriage.
On the other hand, perhaps Uncle Matthew is thinking strategically. If a Patriot family and a king's man family can come together, then perhaps that will insure them to some extent against any future conflict that may break out in the colonies.