My grandfather was heavily involved in the local organisation of the National Party (our counterpart to your Republicans) for decades, then stood for a Christian party in two elections, unsuccessfully. Basically he worked for decades doing what he could to be a solid Christian witness within the political system, in different ways. And all that time, despite the solid work of himself and many others, the country still slipped further away from Christianity. Hence his eventual move into overt Christian politics, since as the main parties became more secular and Christians were marginalised, eventually they formed their own political movement, which unfortunately has been ravaged by infighting and controversy, never achieving anything much sadly. I stood for a different party in a later iteration of this Christian political movement, which was again unsuccessful.
All our countries are on an unstoppable slide towards a political system that will be bad enough to be that prophesied to come before the return of Yeshua. We cannot reverse this, because it has to happen. Things are just going to get worse and worse until Christians are faced with the death penalty, and then things will get better rather spectacularly...
Andrew, I entirely agree with you on a grass-roots level. Regarding political action in America, I'm interested to see how the libertarian party gets on in the USA, but I can't see it being successful, because that isn't the overall agenda. In the slim chance that they are successful, they will become subverted by the same evil influences and be ultimately turned against Christians, including Christian polygynists - simply because there is a bigger story that has to play out, and will happen one way or another, through whoever is in power. The same goes for Trump.
This might sound pessimistic, but I don't actually feel the slightest bit pessimistic. I'm very optimistic. I believe we live in very interesting times, and have amazing opportunities in these times. We just need to recognise the times in order to see the opportunities and not get distracted from them.