Some of this seems like interesting potential sources for conflict. Think about the most right-wing position a decent and reasonable person can hold on a controversy to do with race or LGBT issues, and that can be part of a conflict when someone is upset about the view.
On how conservatives will interact with trans people, there are going to be different responses and opinions from conservatives. Some conservatives view it as a mental health issue, the equivalent of something like anorexia or body integrity dysphoria. For various reasons, it's going to be difficult to depict someone who holds this view as a good guy, unless part of the story is the bigot realizing the error of their ways.
But there is a wide spectrum of other views that someone on the right can hold, from complete and total acceptance to ambivalence.
Regarding the potential conflicts between conservatives and people of color, it is worth noting that a big change in recent politics has been white liberals moving to the left, so members of minority groups, while still to the left, tend to be more moderate and accepting of different views.
https://www.vox.com/2019/3/22/182598...ing-trump-2020
The available studies suggest the majority of third trimester abortions are not due to reasons of fetal health/ the health of the mother.
https://onlinelibrary.wiley.com/doi/...0.1363/4521013
If this were just about situations with serious medical complications, that would allow abortion opponents to agree to carefully established medical exceptions while pushing for a ban in other situations.
I did mention electronic/ online voting. This is something liberals generally advocated for, until there was a greater recognition of the potential downside of hacking.
If we're going with 1970 as the beginning, and looking at issues where conservatives and liberals were on different sides (so conservatives wouldn't get credit for George W Bush's work on AIDS in Africa as this wasn't really a partisan issue) there are some example of conservatives on the correct side, like allowing the use of DDT to combat Malaria in Africa, the Reagan doctrine helping end the Cold War, the greater choice for parents with charter schools, and the rise in policing to push back against the rise in crime. It's hard to appreciate how bad it was; the murder rate in New York City in the early 1990s was about four times what it currently is.