It's not that Manchin or any of these candidates are pro-gun, it's that it is an election year and their constituents are very pro-gun. Essentially, if you get a pro-gun judicial nominee especially one who you can get through without other baggage such that you can probably do it with just republican support, then you put them (Manchin, etc....) into a position where if they vote with their heart or their party then they tick off the majority of their constituents, and thus increase the chances that their republican challenger will win the election. If they fold and vote for the nominee, then you've lost nothing and can point to bipartisan support for your nominee. Just a way to use the appointment process to either gain a senate seat of two or to cement consensus on appointment.
Of course this works the opposite way if the Republicans go open overturn Roe v Wade then they set themselves up to lose senate seats and probably lose the chance to get the nominee confirmed. They won't do that. The closest they will come is to nominate a pig in a poke candidate with no real judicial record but the hope that they would overturn Roe v Wade and that they would also be conservative on other issues - that is a stupid way to go as you could end up with a Bork, Souter, Kennedy, or Roberts type again. But then again both parties are very adept at snatching defeat from the jaws of victory.