Until Trump proves otherwise, I'll continue to think he's not going to act like current Republican leadership, because he didn't act like that during the primary or general election and his platform doesn't line-up with someone who would be against self-driving vehicles.
But what is he saying in private to people like Peter Thiel? We have no idea... And amusingly, Hillary was heavily criticized by Trump proponents for stating the obvious about public vs. private stances. Every bit of Hillary's private talks was dug up, but we know essentially nothing about Trump's real intentions. (Maybe Wikileaks could get on the case? Hah.)
There's a lot to dislike about him and I don't think it's fair to speculate on positions of his he's given no evidence to merit speculation on.
One might make subtler arguments about how this (and much) technology indirectly benefits all of civilization in myriad ways, even in the face of causal fallout like that mentioned above, but we have not one scrap of evidence that subtle arguments will either be employed or considered.
He could well be anti automated driving vehicles, it is widely accepted that one of the first casualties of the introduction of automated vehicles will belong distance lorry drivers. There are approx 3.5 million drivers employed in the US right now, even if we see only 25% of jobs going in the next 10 years that is an extra 850,000 unemployed people. And not only are they unemployed but their skill set is no longer required, so they are either long term unemployed or they need to retrain. I imagine many will be older people and they will not be in a position to retrain significantly, so they become competition for low paid manual work, further depressing wages in this sector. So even if you do get a job the wage is likely to be much lower than that of a truck driver.
These could be protected (for a while) if they introduced anti-automation policies and laws. This sort of short term thinking is right up the republican street.