When talking to conservatives or anyone who does not believe as you do, it is necessary to reframe you arguments in terms of what is morally important to your audience. To further this goal, here are some of the arguments that will have a chance of swaying opinion toward meeting in the middle.
Russia interfered in our election. - Russia interfered with our freedom to choose (freedom) and violated the sanctity of the vote (sanctity). By allowing this to go unchallenged, Trump is betraying the freedom of the American people.
Trump's conflicts of interest - There are rules laid down by the founding fathers (respect for authority) about conflicts of interest to stave off tyranny. Trump is violating those rules for his own greed (moral corruption).
Universal Healthcare & Obamacare- "Conservatives were more likely to support universal health care when they read an argument said more uninsured people led to “more unclean, infected, and diseased Americans.”" (purity)
Immigration - Immigrants love America enough to leave their country and become Americans (patriotism). They break fewer laws and are model citizens. [If proof is needed, bring up the Wall Street Journal article that explains the lower crime rate. Immigrants are 40% as likely to commit a crime as a birthright citizen.]
Reproductive rights - Women are the authorities on their own bodies. We can either respect their authority or violate their trust. (respect for authority, sanctity)
Muslim database - Our country was founded (respect for authority) on religious freedom (freedom). Muslim Americans are no less patriotic than any other citizens (patriotism).
Criminal Justice Reform - Officers with clean records are in favor of reform. (Respect for authority, purity)
Climate Change - Pollution corrupts (purity) our environment. Pollution is a disease of our own making.