To help someone is a moral choice, and individual one. It's a proactive decision.
You argue that Christians are obligated to vote to force someone to make that choice.
This bolsters my point.However, at the same time you are also to pursue compassion and justice in your actions. You do this in your individual actions, in your communities, and in the voting booth. As I stated earlier, you cannot use the government to endorse, promote, or compel adherence to your specific religious beliefs. However, your actions in the voting booth and at the town hall can and should be reflective of your beliefs and conscience.
For example, in a representative democracy, if your government that represents and and that you elect was engaging in genocide, you could not say that well the bible only talks about what I do individually and my voting and my petitioning of my government is excluded from that.
If your country is committing genocide, and you have a say in it, your vote to support it represents an individual moral act on your part. You're putting your personal approval on something which is against the teachings of Jesus.
If you did nothing to support it and indeed try to save people, then your government's actions have no moral weight on your soul.
If you vote to impose your own views on others, then that, too, is putting your approval on something against the teachings of Jesus. You're not dusting off your sandals; you're imposing your will by the sword.
So yes, you are imposing your religion on others by forcing them to act according to your beliefs.
This presupposes that putting anyone under the authority of anyone except God -- whether a dictator, or those by elected majority -- is God's idea of "justice" and "compassion." I don't find any support for that in Jesus's teachings.That is just not how it works. We are all to pursue justice and compassion in all of our actions.