I do not believe that all religions are the same. I see no reason to believe
this to be true. Any faith has two sides to it, the exoteric and the esoteric teachings. When you read the esoteric experiences from around the world you find a great deal of similarity between people of different belief systems. An example of this is St John of the Cross who describes a Kundalini experience much like that of a Hindu.
How exactly do you reconcile "there is no salvation outside the Church" with any salvation claims outside whatever church we're talking about?
For most of human History most people came in to contact with one belief system eg muslims for the most part were around muslims and Christians were around Christians. Survival was never a given for most people, most of the time. Most had to work hard and long hours just to live.( After the hunter gathers stage people seemed to have a less time )
The Exoteric side of Religion was used to suppress the poor.The teachings are both different from other faiths and have been hurtful to people... But... if the the claims of the mystics are true. ( As I know parts of them to be true from my personal experiments in the area of meditation ) The esoteric side of faith is a help to make life have more meaning.
If one is to learn the path of the mystic we must make a considerable investment of time. For a Christian to experience what the Lord Jesus said
"I came that they might have life, and might have it abundantly" (John 10:10). He had to follow the methods of the Christian Mystic. The same is true of a Muslim Sufi on the path of Islam. There was not so much time to learn the ways of others they did not come from the same culture or understand the same language.
How do you reconcile the Christian claim that Jesus Christ is God the Father's only-begotten son with the Muslim claim that God has not begotten any son?
This is not the whole story. A Sufi Muslim seeker may be led to abandon all notions of dualism or multiplicity, including a conception of an individual self, and to realize the Divine Unity. They have divine union with God in this life. A Christian mystic goal is to have communion, identity, or conscious awareness of God through direct experience, intuition, and insight. If both the sufi and christian mystics want the same thing. Maybe the the external doctrines are not so important. Because both can become One with God.
How do you reconcile Abrahamic Heaven, Hell and Final Judgement with Dharmic Karma and reincarnation?
Many orthodox Jews today and in the past believe in a kind of reincarnation. Many Hindu's and Buddhist believe in some kind of Hell and Heaven. There is some overlap in this area. Thats not the point to the Mystic.
Christ said the kingdom of heaven is at hand. Paul said
It is not I who live but Christ who lives with in me. Dirict experience of the divine in the here and now is the point of all the world mystics. To many Hindu's reincarnation is just an illusion of the mind.
When you divide religion into two camps the esoteric and exoteric. For us Hindu's with our interests of unity, it makes a lot of sense and It helps us to be much less judgmental of others. I think it is a very healing view of the world of religion.