Many Christians emphasize the importance of having an actual relationship with God/Jesus as opposed to merely being religious.
Christianity is a religion. It has a clearly-defined doctrinal structure, an established set of fundamental beliefs about God, reality, truth and the hereafter that distinguish it from all other religions, and various practices and rituals that also shape its form and character. But the Christian religion is the context within which a relationship with God is established and enjoyed. Religion by itself - mere belief and ritual - is not all that God offers to us in and through the Person of Jesus Christ.
But what about when people from other religions claim to have similar personal relationship experiences with their deities? For example, a Muslim claiming to have a personal relationship with Allah, a Hindu claiming to have a personal relationship with Brahman, a Hare Krishna claiming to have a personal relationship with Lord Krishna, a New Ager claiming to have a personal relationship with the Universe, their spirit guides, their higher self, etc.
This is where personal experience is seen to be the insufficient basis that it is for truth-claims about the Christian religion. Many Christians (Christian philosophers, in particular) adhere to the "correspondence-to-reality" approach to truth. An important part of this approach is the explanatory power of the Christian faith; that is, the ability of the Christian religion to explain why reality is the way it is. Among the religions of the world, Christianity offers the best explanation of reality, which necessarily entails that it correspond better to reality than all other religions. For example, the Bible doesn't tell us that the earth rests upon the back of four giant elephants that are standing on the back of an even more massive turtle. Instead, the Bible says the earth hangs upon nothing, sitting unsupported in space, just as it actually does. The Bible tells us that reality - all space, time, matter and energy - began a finite time ago in the past. This corresponds exactly with mainstream science. We know that something cannot spontaneously generate from nothing. We don't see horses, or airplanes, or books popping into being out of nothing. No, instead reality is such that anything that begins to exist must have a cause of its existence. The Bible tells us that the First Cause, the Uncaused Cause, of the universe is God - not some bearded, oversexed, toga-wearing Greek superman who throws lightning about from a mountain top, but an inconceivably powerful spirit-Being profoundly unlike us and yet still personal and knowable. This can be deduced very readily from the beginning and nature of the universe. The Bible tells us the human heart is profoundly and naturally wicked. A quick survey of the savage, violent, dark record of human history bears this out very well. And so on.
It is from a superior explanation of, and correspondence to, reality that the Christian religion offers that I speak to people of other faiths. My personal experience is just "icing on the cake," not the primary basis from which to contend for the veracity of the Christian faith.
Qualitatively speaking, what sets the Christian relationship with God apart from relationship experiences that people claim to have in other religions? What makes the Christian relationship with God special and unique? Are people in other religions just having counterfeit, deceitful experiences?
If the Christian faith is true, then, yes, people of other faiths are, generally, having false experiences of God. They are, in reality, either self-deceived or experiencing a demonic counterfeit.
I once saw news footage of a Buddhist priest immolate himself in a roadway in India in protest of societal decline. So convinced was the priest of his religious perspective and the need for such a terrible display that the prospect of an agonizing death could not dissuade him from the fiery protest he had planned. Surely, he was far more persuaded of his worldview and far more dedicated to it than most Christians are to their own faith. If we were to judge the correctness of his religion on the basis of his commitment to it and on the degree to which his religion shaped his life, we would have to concede his religion was much more true, more correct, than the religion of the majority of modern-day, half-hearted Christians.
But there are nominal Buddhists just as there are nominal Christians. Few Buddhists would go to the lengths of the priest I just described. What does this mean, then, for the truth of the religion? It's clear that mere strength of conviction, a powerful sense of the reality of one's beliefs, is not itself enough to establish one's beliefs as true.
We all know of people who were/are very sincere and fully-convinced of things that were/are quite in error. At one time, the majority of people in Europe thought the world was flat, right? They thought, too, that the Sun revolved around the Earth. Many Europeans were utterly convinced these false things were true, persecuting severely those who disagreed.
It's a very bad idea, then, to try to argue primarily or solely for the truth and reality of the Christian faith on the basis of personal experience, or from the strength of one's conviction about that experience. The veracity of the Christian religion has to be established on better, more objective, grounds. This isn't to say that a personal experience of God should be left out entirely from one's presentation of one's faith to others. Not at all. But the weight of that experience is felt best only after solid, objective, true-to-reality grounds for it have been well-established.
Lastly, how can a Christian evangelize or witness to a person who claims to have a "personal relationship with God" and all sorts of spiritual experiences in a different religion?
It depends upon the individual person to whom one is offering testimony of the reality, the truth, of the Christian faith. I don't think there is a one-size-fits-all approach. Some may need significant apologetic information; others may require only an account of one's personal experience of God; still others may need a combination of both. What is required, though, in
every instance of evangelism is
prayer and a holy, God-honoring life. It is God, after all, who "gives repentance to an acknowledging of the truth." (
2 Timothy 2:25). He is the One, in the Person of the Spirit, who "convicts the world of sin" (
John 16:8). God is the One who draws people to a saving faith in Jesus Christ. (
John 6:44). And so, in evangelism, we must be looking to Him in prayer and walking with Him as "vessels sanctified and meet" for His use (
2 Timothy 2:21); for it is only the prayer of a
righteous person that "avails much" (
James 5:16).
