Queen Elizabeth was never political and since Queen Victoria ruled, her decedents have avoided politics. When you rule as queen or king you rule over everyone, so you should typically keep your opinions to yourself... King Charles would be wise to follow that same tradition.
Time will tell. But I think the real test will be William. If he's a crappy Monarch, the British might go ahead and dismantle the institution. In other words, it doesn't really matter what Charles is going to do in the meantime.