Here is how I would handle this.

Dear Governor:

I voted for you. But I don't agree with your stance of trying to limit my constitutional right to bear arms. There are many more people who voted for you that think the same. Not all of your constituency thinks that limiting a persons constitutional right to bear arms is a good move on your part. You may think that those people will knee jerk vote for you because they did before. But you might anger them enough to not support you again. That does not mean they will vote for the other guy. But by making me or many others angry, we may not vote for you at all. Which is just as bad for your job in the long run. Not all liberals or Democrats are anti gun and don't assume that we will knee jerk vote for you if you decide to limit our rights rather than defend them.

Have a nice day

Now do you guys see why having liberal gun owners is a good thing? Who do you think he is going to listen to. Someone who would never vote for him or someone that would and did. Remember gun rights is bigger than your disdain for one side. Don't hate those who stand with you on some subjects because they don't see eye to eye on all of them.