My observation has been there are basically two ways traditional conservatives have historically dealt with this issue, neither of which has been particularly successful.
1) They just say "Well Jesus was oppressed, Christians are always going to be oppressed (even when they are in control), the world is sinful anyway because of Original Sin, so just pray for deliverance while accepting your shit situtation."
This was used to keep serfs, slaves, and peasants from revolting, while 'divine right of kings' allowed the upper classes to use Christianity to bootstrap their own power, often while crushing 'pagan' or 'heretic' sects/groups. Which is why it no longer has very much moral power in the eyes of many, and Enlightenment/classical liberal thinking has by enlarge abandoned trying to use Christianity religion as part of it's social tool kit. When things like the All Hallowed Eve earthquake in Lisbon back during 1755 kills 80k on one the holy days, and was followed by a tsunami that compounded the damage, is really makes people not see religion as anything worth leaning on for guidance. It was that event that inspired Voltaire, and those who came after, to revolt against religious 'moral authority'.
2) They claim "If you have a problem with the system we support, it's probably you that is wrong, for [X reason]. Repent, pray, and maybe the system will find a place for you or you will come to accept the system."
Never mind that Christianity has been used to excuse some pretty heinous shit, the system was often full of graft, corruption, and 'indulgences', along with things like the 'Catholic Preist touching boys scandal', and stealing/rebranding 'pagan' holidays as their own. Liberalism, and socialism, don't try to claim a 'divine mandate' as it's justification, and that is no small thing. A material world justification for their aims, instead of harping on about Original Sin, damnation, and 'Judgement Day', reach ears that no longer trust religious authorities.
Traditional conservatives do not have good answers for these critiques and problems, because their go to answers only preach to the already converted. Those answers do little to address how these issues look to the younger generations who find religion to just be another set of self-interest, self-justifying authoritarians who have historically been far less righteous than the person they claim as their savior.
Ghandi once said something along the lines of "I love your Christ/his messasge, but not Christianity, because so many Christians are so unlike their Christ." Too many try to convert others via the sword, hellfire sermons, or appeals to ignoring the harm Jesus's followers have perpetrated. Too few go the route of showing Jesus's message in the actions, instead of simply preaching his words and those of the...lets be blunt, most of the Bible is fanfiction or a 'dramatic recitation/retelling of historical events', at best. Christianity does not have a monopoly on righteousness, not in the current time at least, which is why relying on appeals to it to sway people's politics is not a dependable avenue.
I say all this as a person who believes Jesus was part of the divine and has a very worth while message, but does not see the 'Christianity' that resulted from his sacrifice as something Jesus probably would want to be a part of. Nor do I believe that people of other religions are cut off from the divine either, simply because they look to other figures besides Christ.