I mean I can believe both of those sets of people exist, but hardly that they're numerous enough to dictate the election strategy.
I don’t think libertarians realize where we are in 2020. Lots of culture war stuff from the last few decades where libertarians sided with liberals (abortion, contraception, same-sex marriage) has now flipped and then battleground is keeping the government from forcing people to participate in those things: Catholics being forced to perform elective abortions, nuns being forced to pay for contraception, people being forced to participate in same-sex weddings as bakers (and presumably caterers, etc.)
Nearly all EU countries recognize such conscience rights. Eliminating them would put the U.S. squarely outside the mainstream on this issue: https://en.wikipedia.org/wiki/Conscientious_objection_to_abo... ("Conscientious objection is granted in 22 member states of the European Union plus the United Kingdom, Norway and Switzerland.").
I guess it’s the libertarian thing. Your right to swing your arm ends at my nose.
And, of course, since the doctor is also an active participant in killing the fetus, it’s not the “doctor imposing morals in the patient.”
Obviously not. To begin, no religion I’m aware of would preclude informing the patient in that circumstance. And few libertarians believe that individual freedom requires allowing deception of others, as in your hypothetical.
Apart from that, weighing individual liberty interests is always context-dependent. E.g. consider the various wrinkles when it comes to self defense. For a libertarian, forcing doctors to perform a procedure that involves killing something (whatever you think that thing is) in non-emergency circumstances just because that might leave too few people in an area willing to do that probably falls too far on the side of ignoring individual liberty. It’s the basic libertarian position: you may have a right to something, but you don’t have a right to make someone else give you that thing.
so the solution is to ban abortions, contraceptives, and same-sex marriage altogether?
Look at the political debates likely to come up over the next 10 years and tell me where libertarians are aligned with liberals. Apart from the things I mentioned above, cases that will come up may include the constitutionality of a wealth tax, changes to equal protection to allow discrimination in favor of particular groups, firearms confiscation, etc. (I’m not saying all of these will happen, I’m pointing out what the next legal battlegrounds will be.)
The difference is that—unlike racial justice, women's rights, and gay rights—in this case abortion was a mistake and so the step forward would be to reverse it. If you go back far enough, society has successfully reversed actions that were at the time considered forward progress.
Also, I think most of the "right libertarians" are already Trump votes out of sheer disgust and exasperation. Libertarians (of any stripe) are probably the least likely to get hot and bothered by Trump's antics.