Yes, Christians believe we have free will to choose to do what is right. Choosing to do what is wrong would be destructive and a false freedom.
As for forcing my conscience upon others, it depends what you mean. I think abortion must be legal because look at the alternative - more death. So in practical terms I'm not forcing that at all (though I might if illegal abortion wasn't potentially harmful to women).
There are some practices that a believer in any faith will observe for themselves only - like not eating certain foods. There are other practices that they believe (and this is on a spectrum) should apply to others as well because the alternative behaviour is morally wrong and harmful, either to the people involved or others.
Most of us have moral beliefs about how other people should use their bodies, and these are reflected in the laws we hold. I don't support your right to sell your kidney, to sell yourself into slavery of any kind, to inject yourself with harmful substances, or to supply them to others. I think absolute bodily autonomy is not widely supported by pro-choicers either, as the reaction to Sarah Catt's full-term abortion showed (although, despicably, the moral position tends to be completely different for Down's Syndrome, which is, far far removed from the kind of condition offering 'no quality of life' that is used to justify this principle in theory).
So I don't think many of us are completely happy for everyone to do what they want with their own bodies - at some point, we start to interfere, or we think the state should.
Christians, like believers of other faiths and many responsible members of society, care about the behaviour of others when they perceive it to be harming others in society. It's important that someone does give a damn in this way, because we are not just individuals, but a community with a collective sense of morality. We all want to have a voice in defining what we allow and don't allow. We have to have it - look at the occasions in history when people haven't challenged commonly held views that were clearly harming others. To some extent I think we all agree that 'evil flourishes when good men do nothing' - as would be shown if selling our kidneys became legal today. Christians aren't particularly interfering or unusual in principle I don't think.
However I would add the caveat that a Christian on the look-out for signs of 'evil flourishing' should be looking for an absence of compassion in their own behaviour and attitudes before considering wrongdoing elsewhere. That's the primary evil we are told to avoid.