It's interesting to me that you bring up abortion, since to me, as an outsider (I'm not from the US), the mainstream US debates about abortion and about guns have a lot of parallels. The "against" side tends to paint their proposals as "reasonable, common-sense regulations" but their more extreme arguments tend to be full of misinformation, misunderstandings and emotional pleas to the sanctity of life. On the other hand, the "pro" side either believes that all those "reasonable regulations" are just a transparent attempt by the other side to get their foot in the door, to move the overton window a little bit, so they can enact harsher regulations later, or that those regulations are not reasonable at all and will never be implement correctly.
For example, whenever the pro-choice side hears someone from the other side propose regulations about requiring permits for clinics that perform abortions (something that in principle they might agree to), they fear that the person proposing the regulations isn't really pro-choice but only says that because outright banning abortion would not be politically feasible, thus they fear (rightfully so, since it has happened) those regulations will be so onerous or badly implemented that it will result in a de-facto ban on abortion, maybe those permits will be very hard to get or maybe the organization handing them out will be understaffed and underfunded (or both). Similarly, whenever someone who is pro-guns hears someone talking about mental health checks before owning guns (also something they might agree with in principle), for example, what they fear is that this system will be abused to deprive as many individuals as possible of their rights without due process.
Thus, in this situation, neither debate will move forward because pro side does not believe that the anti side is proposing any legislation in good faith, and the reason they believe so is that in many cases that has blatantly been the case, leading to farther spreading of the divide.
Additionally, as you say, someone might be both pro-choice and pro-guns but the political situation is such that they have to choose one or the other, and thus they choose the one they hold dearer to them, usually one that affects them more personally. Unfortunately for the pro-choice crowd, gun control laws seem to personally affect more people in the US than abortion laws.