In Egypt, he allowed the dictator previously supported to fall. This is specific to Egypt, and has caused some issues, none of which are terribly important to the US at this time. Other presidents have done different things in different countries because it probably made sense at the time, in that particular place. Letting dictators fall is rare, even though it has been done when the dictator tried to bite the hand etc. I'm not familiar with any hand biting in Egypt.
Probably the largest venue in which we let ideology get in the way of "good business" has been with China and its human rights record, but even there he has been much more vocal about things like Chinese theft, Chinese cyber attacks, and in Asian sea disputes which has strained relations anyway.
Before I go any further, I don't recall you talking about Sudan and Reagan...what was your point there? Because as you know, Sudan was at most a pawn in issues relating to Ethiopia. And the Leadership in Ethiopia making close connections with the Soviet Union. If you're talking about Reagan possibly picking winners and losers in a peripheral fight in Ethiopia, then that isn't exactly the same as letting hand picked dictators fall.
I mentioned Sudan under Reagan which I mentioned the last time we discussed Egypt, because it is located in the same geo-political region, and was part of our triple alliance between the US - Egypt -and Sudan.
I reference the Nimeiry Administration which was probably the most pro-US administration to ever exist in the Sudan, and one that fell to populist protests / demands for democracy while Reagan was in office (the military intervened to form a transitional government much like Egypt's military did).
Despite how heavily we relied on Sudan to check Gaddafi's growing influence in Chad and his moves in eastern Libya (Sudan is a historical and current weapons smuggling route to both the Middle East and North Africa) the US has to and did, under Reagan pay homage to a more democratic process even though it left us with a leader who was much more adverse to the Untied States, not to mention the subsequent toppling of that administration by Bashir in 1989 (a coup which took place under HW Bush).
President Obama pretty much followed the same standard course with Egypt, only we've maintained better working relations with the end result (Sisi's government) than we managed to with the end result in Sudan (though we still do share intelligence there).
I also think that saying that we "let him fall" rather suggests that we had more control over the issue than we actually did. It would be like saying that Reagan "Let Nimeiry fall" when I think it would be more appropriate to simply say that we rolled with what was largely happening on the ground and defaulted during unstable times to our general talking points which favor democratic reform.
We saw the same process under HW Bush in Africa starting in 1989 and especially in the early 1990s with the fall of many of Africa's notorious big men (even those that had been aligned with us during the Cold War). Kaunda fell in 1991, Siad Barre also in 1991, etc
Under Clinton Hastings Banda fell in 1994, Mobutu Sese Seko in 1997, etc.
Under Bush W: Pervez Musharraf fell in 2008.