I wouldn't be so sure that Humphrey would be end up regarded as an enemy of the anti-abortion movement.
First of all, that was before
Roe v. Wade. A lot of people had previously had fairly good relations with the right-to-life movement before
Roe but it became harder to do so when it required repudiating a Supreme Court decision (and in this case it would mean a decision in which Humphrey appointees would almost certainly have joined). Once
Roe was the law of the land, being "personally opposed" to abortion was no longer enough. And "leave it to the states"--a popular position among Democrats and Republicans alike before
Roe--was now impossible (at least without a drastic change in the Court) without a constitutional amendment. Humphrey opposed such an amendment in OTL:
https://www.nytimes.com/1976/04/25/archives/humphrey-offers-views-on-abortion.html
Second, even before
Roe, Nixon was proving to be friendlier to the movement than Humphrey was:
"Some of Nixon's advisers—particularly Pat Buchanan and Charles Colson—told the president that a conservative stance on abortion might help him increase his share of the vote among conservative Catholics. Nixon seemed eager to follow their advice, not only for political reasons, but also because much of the support for abortion law repeal came from a culturally liberal, feminist left that he personally despised. In April 1972, he told White House aide H. R. Haldeman in a private White House conversation that abortion, along with marijuana use, was an issue that he wanted to "hit ... hard" in the upcoming presidential campaign. The next month, when Rockefeller's commission recommended the legalization of elective abortion as a way to reduce population growth, Nixon immediately repudiated the suggestion.. He was quickly becoming a president that the pro-life movement could support.
"Not content to rest their hopes on a single party, pro-lifers then turned their attention to the Democrats. After Muskie dropped out of the race. pro-lifers were left without a reliably pro-life candidate. The two remaining frontrunners for the nomination—Senators George McGovern and Hubert Humphrey—had hinted that they were in favor of legalizing elective abortion. Pro-lifers knew that both candidates were facing strong pressure from abortion rights supporters within their party, but they hoped to counteract that pressure with a show of strength from their own side. Humphrey seemed like the better target. In June 1971, the Minnesota senator told the NRLC that he was opposed to abortion, but in October, he backtracked, telling the press that abortion should be a matter "between the woman and her doctor." Pro-lifers responded to Humphrey's shift with a barrage of letters. Humphrey again vacillated and promised to release a statement clarifying his position. But he never did... "
https://books.google.com/books?id=FKfTCgAAQBAJ&pg=PA185
BTW, Nixon's conduct should put to rest the notion some people here have that the GOP didn't try to make an issue of abortion until 1980. Have such people forgotten "acid, amnesty, and abortion"?