I can only really think in any depth about US universities, based on personal experience. The major shift in ideological orientation came in the humanities, starting in the 1960s, accelerating with the development of the "New Left" in the mid- to late-1960s. There were plenty of cultural vectors pushing university culture to the left at that point, but the biggest accelerator, IMO, was the anti-war movement.
In order to at least put the brakes on that process a little bit, one would have to make significant changes in the course of the Vietnam War, either getting the US largely out of the conflict before c. 1966 or so, or somehow creating the conditions for a major escalation of the effort and changes in basic military policy by then and certainly by no later than Tet in '68.
In terms of what happens after that, you'd have to see some kind of invigoration of non-leftist political culture on a broader front earlier than it happened in OTL in order to produce influences on university culture in time to at least partially offset the generational impact that the students of the New Left had as they entered their faculty years in the late 1970s and into the 1980s.
Although I think it's not well understood by folks on the left in the US, one of the big amplifiers of the "culture wars" in the US was the impact that the New Left students had as they entered into faculty positions in US universities. Although there were inklings of a cultural reaction from the right before this, it was when the young academics whose background was experience as undergraduates in the New Left period started to have influence in academia that really got the attention of writers and other "culture workers" on the right in the US.
So, to develop an answer to the OP question for trends in the late 1970s and especially in the 1980s, one would have to imagine some kind of intellectual and cultural "seedbed" for the right at an earlier period, that would generate its own cohort of academics to enter the university as faculty during that period. In OTL, the right has been unsuccessfully playing "catch-up" on this score since the late 1970s. To have a different outcome, you have to give them a better head start in generating their own "bench" at an earlier time.