I agree with those who say you can't see this only as a refusal to vouch for your character. If he refused you, and vouched for someone else, then fine he is no friend, but that isn't the case here.
You cannot divorce his refusal (or potential agreement) to be a reference from his views on guns. He apparently thinks guns are dangerous, dangerous enough that people shouldn't have them around, and has bought into the idea that carry is inherently dangerous. Then you ask this guy who thinks people carrying guns makes life for everyone more dangerous to agree to be a reference to allow you to do something he is morally and ethically opposed to and take it personally when he doesn't?! I would say, it is to be expected.
A question for those who say they'd end the friendship over this, if he was a real friend he'd have trust in the OP's character and judgement and override his own moral views and sign on anyway...
This will work best for those who are pro-life, if you aren't you can try to think that way for a moment.
You have decided that abortion is murder or at least morally wrong. A friend you respect asks you to drive her to a clinic because she needs an abortion. It won't give her the abortion, but it will make it possible (just as a reference won't give a person a CCW but it isn't possible without it). If you don't, someone else will probably give her the ride (just like the OP was able to get another reference) but she asks you because she spends a lot of time with you and trusts you. You are morally against abortion and think it should be banned, but she thinks you should overlook this in this case because you are friends (or at least solid acquaintances) and should trust her character and judgement. Would you give her the ride?
For most, I'd assume the answer is no. You may trust her character and judgement, but that doesn't change that you disagree strongly with her judgement in this case and at the very least you probably don't want to be a party to something you so strongly oppose. Further, you may even feel she crossed a line and be a little upset that she'd even ask you knowing how you feel and put you in that situation where you have to choose between your values and helping out a friend. That is the exact situation the OP and his friend/acquaintance were in.