It does not preclude a Christian from spreading the gospel. Christians can walk and chew gum at the same time. It certainly is a timely and serious issue.
No, but it creates the impression that those who sign it are doing the "most important thing" a Christian can do. Protesting an abortion clinic is easy. Standing up for traditional marriage is simple. Supporting freedom of speech is part of being an American. They are all good things, but they detract from the most important thing. Witnessing and making disciples is THE most important commission.