Let's consider a specific example. Should "In God We Trust" be printed on all of our money? Does that really matter that much? If individually we trust in God shouldn't that simply show itself in our actions? Conversely, if we don't trust in God that could also show. Does it send a false message to both the world and also to (potential/hypothetical) future generations that might dig up the remains of our civilization and find it on our money? I think it is much more important to live a God-trusting life than to try to force others to even when they choose not to. Arguing close-mindedly against ever removing the phrase from our money probably hurts theism and Christianity more that it helps. Stopping to understand, stopping to think critically, and stopping to be open-minded is bad practice.
The concept of changing hearts doesn't simply have to apply to politics or religion or the like. Changing hearts can also apply to our lives in a general sense, regardless of our goals, mission, vision, or causes. If we simply argue based on ideals and don't actually live up to them or have a character that supports the types of things we support, then we won't be likely to change hearts or minds. People need to see something different before they can ever think about changing their mind on something. Even if they never change their mind on something, they may be able to have a change of heart toward specific situations. Persistence is one key to success. Let's take an example from the Bible. In Luke 18, verses 1 through 8, we find the parable of persistent widow. It reads:
"Then Jesus told his disciples a parable to show them that they should always pray and not give up. He said: "In a certain town there was a judge who neither feared God nor cared about men. And there was a widow in that town who kept coming to him with the plea, 'Grant me justice against my adversary.' "For some time he refused. But finally he said to himself, 'Even though I don't fear God or care about men, yet because this widow keeps bothering me, I will see that she gets justice, so that she won't eventually wear me out with her coming!' " And the Lord said, "Listen to what the unjust judge says. And will not God bring about justice for his chosen ones, who cry out to him day and night? Will he keep putting them off? I tell you, he will see that they get justice, and quickly. However, when the Son of Man comes, will he find faith on the earth?"
So, even though the judge didn't fear God or care about men, he appeased the women so that she would stop bothering him. Being persistence in our love or actions can make a much bigger impact than simply stating a case for something (and then not even bothering to live it out).