You are always given the advice that this ia a really bad move if you go against the ERA. Maybe the advice in the game is completely worthless. Of course why even include the question if both candidates are always supposed to answer it the wrong way?
Reagan went against the ERA, ran a competitive campaign in 1976 and won in 1980 and 1984, and once the amendment failed no attempt whatsoever was made to revive it, so my take is that this was a weird moralistic overreach amendment like the 18th, except the 18th actually passed, but the ERA probably would have the second amendment to be repealed later if it had passed. Presidents have nothing to do with amendments to the constitution so the proper response of candidates to proposed ones is not to comment at all.
You are given advice that it is a bad move only as Carter. As Ford, you are told that it upsets some women voters but also fires up the party base, its far from presented as a really bad move
And sure, Presidents aren't directly involved in amendments, but some still give public support for amendments. It isn't like Presidents or candidates have always just not commented at all, iirc Nixon openly supported the ERA, Gerald Ford OTL spoke out for it, and Jimmy Carter himself did have some involvement not just verbally supporting it but also did have some direct involvement with signing legislation that extended the congressional deadline. And sure, Reagan won going against the ERA... but, well, him getting about half the vote in the GOP primary doesn't really go against the idea that a sizable but not overwhelming majority of the general public was for the amendment, and in 1980 and 1984, maybe it was just one of those issues that wasn't a big deal in the eyes of the public, especially among the eyes of those who would consider voting GOP, with all that was going on nationally, while in 1976 maybe it would have been a bigger deal for Carter, a Democrat rather than a Republican, to come out against it or not endorse it
And I'm not really sure it makes sense to look at an amendment for equal rights for women as a "weird moralistic amendment" akin to one outlawing alcohol. And if it did pass, even with Reagan being against it and with the conservative leaning Reagan era, I don't know if we'd see 38 states being willing to repeal it, its one thing for a conservative president who isn't all that involved in it (especially once it is passed) to be against it but another thing altogether to get state level majorities who are willing to outright get rid of the amendment - supporting some general social conservatism is one thing, but I could imagine that supporting the repeal of what could become seen as a major civil rights amendment protecting half the population could create more of a backlash once that amendment was enacted and becomes part of the status quo
Anyway, speaking of 1976 elections...
Here's a Ford 1976 win on easy, winning the popular vote by 6 million votes and winning every state outside of the south except WV and MA, plus winning OK, TX, LA, MS, FL, NC, and VA in the south.
And here's a Ford win on normal, rather more narrow in the popular vote, by less than 1 million votes, but winning all the Ford OTL states plus PA, OH, WI, MO, TX, MS, FL, and HI, for a very solid electoral vote win of 370. Both with Ford generally taking a conservative stance including opposing the ERA, and getting in the top 99% of results
And going back doing some as Carter, it looks like just saying it is up to Congress and not commenting otherwise results in a "some wings of the party are pretty disappointed" remark from the advisor, which isn't necessarily the same as it being presented as a "really bad move".
Here's a Carter win on normal, winning by 4.5 million votes and nearly 450 electoral votes, where Carter takes the "its up to Congress" stance on the ERA, that was in the top 99% of results.
And here's a Carter win on easy, winning by 9.2 million votes and over 500 electoral votes, with the same strategy, that doesn't quite get as high but does get to the top 98% of results
So it isn't clear that it is particularly harmful for either candidate. As for why including the question in the first place? Well, its possible to win while running in favor of it too, there could be different strategies to win, like running as as a socially liberal Democrat/Republican as opposed to a socially conservative or moderate one, it could be a matter of different appeals to different parts of the coalitions