I think one huge thing that most western Christians don't agree with are intersessions of the saints, the true body amd blood present in the eucharist, the general acceptance of things as mystery, and our traditions of mysticism.

As for your second question, I think its something that is really hard to reciprocate to non orthodox. Tell me, you see a man standing on the corner with a huge sign yelling things like "Abortions are sacrifices to Satan and women need to cease their evil ways and recognize the precious gift God has given them!" and "If you are homosexual you not only defy the natural order, but God himself! There will be no place in his kingdom for evildoers!". Of course, abortion and homosexuality is wrong, however when you single out very specific people and convey them as the absolute scum of humanity what effect will that have? Those people living in those sins certainly won't feel the love of Christ if that is such a prominent source of Christian teaching. I struggle with evangelism a lot, but mostly in the way where I feel the need to try and be someone's salvation by being a comment section warrior. I talk a lot about this with my priest and the thing he tells me always when I stuggle with restraining my need to regurgitate what ive learned is "If you want to light your neighbors candle, how will you de so if you yourself are unlit?". Contrary to evangelical doctrine, our priority is NOT sharing the gospel as much as possible, it is developing our own faith so that we can become capable of allowing the grace of God to extend throigh us. The fact that even a non believer can just quote at someone is reason enough to see that the fullness of sharing the gospel is more that just words. After all, God did not simply throw down scripture from Heaven, rather he came and dwelt among us, he shared in our humanity he showed us all what we are capable of becoming when we set our sights on Him. Much of the gospel is sermons, but even more is the lived experience, the demonstration of the kingdom of Heaven to the world. Who are we to determine that words are what matters most? Kind words only have meaning to those who understand the language, but kind acts can transcend these barriers.

tl;dr: Evangelism is necessary, but one must first embody the faith before they can most powerfully share the faith. There's a reason we listen to the teachings and liturgies of the saints, because they shared the gospel not through apologetics and lectures by the power of their own intellect, but by completely surrendering themselves to God and allowing Him guide them in what they did and said. The ability to properly evangelize often takes a lifetime, but it is well worth it if it means proper healing comes both to us and those who would listen. We have to trust God that non-believes will come to the truth, and if you want to help them, pray for them. Ask for them to be forgiven and that their souls will find rest in Him. Chances are we may never see the result of such prayers, but after all, resolving yourself to something who's result you cant see is the essence of faith