Denise:
Wow, good discussion!
I believe it is OK and even necessary to bring to the public square my understanding of the Gospel,
With that wording, I would say it is impossible for any person, unless cloistered, to avoid living their life in public according to their faith & understanding of the Gospel of any religion.
But, that is a long way from our General Synod or up-teen conference annual meetings making pronouncements as if any legislators regard our actions as having any authority.
I know some of our Justice Witness Staff personally. I have high regard for them personally. However, I don't see that arm of our Church having any measurable impact. I mean, when there is a disaster, you see our military, FEMA, the Salvation Army, the Red Cross & Pat Robertson's emergency aid teams. We never see Church World Service or the UCC or the Methodists being called or thanked in public.
MY point? If we are going to go into the Public Square, let's do some good that folks will not be able to ignore. Let's do something & show others how to live & serve humanity by example.
(Yeah, I take guff in the UCC for taking the Bible toooooo seriously AND get "Gibbed" by conservatives for wanting integrity and lives demonstrating our faith so the public can see. )
Got to run...
Blessings!
How is that the same or different from a very conservative Christian who would enact laws to implement male primacy (limiting jobs women can get, women's financial roles in families, etc.)?
Well, as possibly the most conservative folk still in the UCC, those proposals have no support from a conservative reading of Scripture. No where did Jesus tell the Disciples to pass resolutions, start boycotts or in any way attempt to change the government or the laws of the land of His era. A Conservative does not attempt to achieve by legislation that which can only be achieved with a change of heart, soul & mind. A Conservative also pays attention to enforceability. While what you are describing does occur in some households, those are not the sorts of things on the minds of Conservatives wish list of new laws.
Most of "us" want fewer government intrusions trusting the power of prayer over the power of the secular State.
Sorry. But, good try, anyways!

A "conservative" example would be passing laws against 5. Disrespecting authority 6. Murder in its various forms of lesser physical harm; 7, Stealing by any means irrespective of technology, this guarantees property rights which socialism disavows, btw; 8. lying whether by omission or commission. 9. Adultery and other forms of intentional violation of private convenants/contracts, if you will. 10 Conspiracy to defraud others as a result of "coveting" their possessions, and other forms of attempted theft.
I left out 1-4, as this is the last 6 of the 10 Commandments.