Third, I find the Christians who preach at military funerals annoying, should I just go up there and start swing swords?
No, of course not. I may not like people such as Westburrow Baptist, but I dont want violence. I want them in jail. With you're first point, I stand corrected. With your second point, Balgruuf is by far my favorite character. I have never picked the Stormcloaks during the Civil War questline, because as my friend said, Jarl Balgruuf is a boss

^Those are NOT Christians. End of point.
Please do not argue that or say otherwise here, because already mentioning that is breaking forum rules about religious discussion.
Also, OT: Heimskr is not stupid, especially since he preaches about a real-life figure, who did ascend to godhood....and furthermore, killing him just makes him a martyr. The only good justification for doing so would be based on his support of the Stormcloaks, though since he's a civilian (and a clergymen) he is not a military target, and his opinions should be respected, as long as he does not aid or abet the enemies of the Empire.