Or maybe that he is a member of one of those weird fundamentalist sects that believe the safety razor to be an instrument of the devil. Or perhaps that his life plan involves a stint as a frontman in a ZZ Top tribute band.
But appearances, as they say, can be deceptive. And just as you shouldn't judge books by their covers, it would be wrong to assume the caveman look that made Strauss one of the most recognisable figures in world rugby long before he signed on at Glasgow is an expression of his inner Neanderthal.
Strauss, 26, dynamites such preconceptions with an engaging manner, a cosmopolitan outlook and an articulate turn of phrase. A late developer in rugby, had his light stayed under the bushel he would by now be well on his way to qualifying as a vet, a career he may yet turn to when his playing days are over.
It is one of the mysteries of the age that Strauss was not offered a professional contract in South Africa until he was 23. After all, it is not as if 6ft 6in Sebastien Chabal lookalikes are exactly thick on the ground even in that land of rugby giants. Astonishingly, Strauss played only one first-team game for his school, and it was only by chance that some performances at Stellenbosch University led to an invitation to a trial with the Johannesburg-based Golden Lions.
Five months later, he was captaining the side. Within a year, he was leading them to a Currie Cup triumph, and getting himself voted player of the tournament for good measure. He then kicked on to become a major and widely-admired player in the Lions' Super Rugby 15 campaign, although the unhappy backdrop to that experience was that the franchise was already in the financial tailspin that led to their elimination from the competition.
Hence his arrival in Glasgow, who won the race for his signature two months ago by offering a longer contract than either the Crusaders or the Chiefs, both southern hemisphere giants, had put on the table. And hence the reason he finds himself in a new flat in Glasgow's west end, one which would probably be described as comfortable if the furniture he ordered a month ago had actually turned up.
Not that he is one for complaining. "I moved in a month ago and I'm pretty happy with it," he says. "It will be nice when I get the furniture too, but I'm settling in well. I'm near Byres Road and there are lots of good little restaurants and young people in the area. I go to the movies a lot."
Ah, the loneliness of the long-distance rugby player. But sympathy for Strauss's spartan circumstances should be restrained, as he will soon be heading back to South Africa to marry Tami-Lee, his long-term girlfriend. As a consequence, he will miss Glasgow's Heineken Cup away fixture against Castres in two weeks' time, although he does expect to be in the side when Gregor Townsend's team take on the French outfit at Scotstoun this Friday.
In some eyes, the tournament is already a lost cause for Glasgow as back-to-back losses to Northampton and Ulster have left them plum last in Pool 4, without so much as a bonus point to their name. The odds are daunting, but in Strauss's eyes they are far from overwhelming.
"I have seen Castres play a few times and they are a good team," he says carefully. "But we are still looking to somehow turn our Heineken Cup season round and get a result. There are still four games left. If we can win four out of four then anything can happen.
"The teams at the top of the pool could easily lose a game so nothing is set in stone yet. If we can win our two games against Castres then I think we can get a bit of momentum, so going through is still realistic."
Spoken like a leader? Strauss's fast-track to captaincy of the Lions has led to speculation that he could soon be carrying the same responsibility at Glasgow. On the day his signing was announced, Townsend drew comparisons with Todd Blackadder's role at Edinburgh almost a decade ago, so the coach clearly feels he has a player who could become a rallying point for those around him.
Al Kellock, first-choice captain for the past few seasons, is now 31, and in an increasingly competitive squad he may be used more sparingly in the future. Is Strauss the heir to the throne?
Maybe, but he is in no hurry. "Coming into a team environment, you don't want to step on anyone's toes," Strauss says. "You don't want to be the new guy who is talking himself up. So I'm taking it easy, focusing on learning all the plays and calls and settling into the team. Anyway, Al is a great captain. I've never heard anyone talk like he does, especially in the pre-game huddle. There are good leaders in the team and a lot of experience in guys like Sean and Rory Lamont and John Barclay. Those guys have all played international rugby, so they have their hands full with leaders already."
And maybe there is no harm in letting Strauss concentrate on his own game rather than the 14 blokes around him. Against Northampton, his first Heineken Cup match, he was voted man of the match, and he picked up his second such accolade against Leinster last weekend. There was an impression of rustiness, edginess even, about his first couple of performances for Glasgow, but he is now well up to speed.
And in his element. "I have enjoyed it. We have been doing well in most games and although we didn't have any luck in the two Heineken Cup games, I think we can still turn that around. It is a good set-up, really professional, and I love the atmosphere in the team."