Not really. He got his start in the newspaper business by inheriting his father's, Sir Keith Murdoch's, already fairly substantial media holdings, and most of his early career (from 1953-1964) was spent supporting the conservative government of Sir Robert Menzies. He then transferred his support to the minor, if anything more conservative, party in the conservative coalition - the Country Party under Black Jack McEwan (from 1964-1972).
He did support Gough Whitlam and the Labor Party in the 1972 election, but abandoned that support before the end of 1974.
In the UK, he supported Thatcher in the 1980s.
He is, as you say, an opportunist - he'll switch sides to anybody who gives him what he wants. But throughout his career, he has tended more to the right than the left, whether because of some actual convictions or just because that's the way it happens to have worked out, I couldn't say. But it's not very accurate to suggest he supported Labor early on. At that time, conservatism was definitely in the ascendancy in Australia (23 years of consecutive conservative rule) and he was playing that game.