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In the new testament (e.g. Romans) Christians are told to submit to governing authorities and Jesus himself said to pay tax. Voting is part of partaking in the governing structures of the day, as unpalatable as most parties are today.
Also the division between church and Christian isn't one the Bible allows, see Hebrews for example. There are religious organisations that call themselves churches but rely on their works rather than Christ's work for their eternal hope, these are not churches and eternity will show it to be so.