Organize, organize, organize. Don't kid yourself into thinking that campaigns electoral or otherwise are battles of ideas alone. There is no substitute for pounding the pavement, shaking your neighbors' hands, hearing their concerns and getting their support. You should expect that your opposition will be doing as much. Don't bash your opponents for their religious views.
Religion is something to be respected and honored.
And while your opposition's political views may flow from their religious views, in the end the battle is over politics and policy. Don't suggest otherwise. Along the same lines, resist the temptation to ridicule or belittle your opponents, either on the grounds of their religion or their political views. They're citizens taking part. They may be wrong on the issues, they may have ideas, even motives, with which you find fault, but they're entitled to be treated with respect.