I completely agree with this. I have frequently read on mumsnet posters saying things like 'I'm Christian but really relate to Hinduism' or 'I consider myself a Christian pagan'. This tells me that these people are often ignorant of Christianity at its core, either due to ignorance or misinformation.
A lot of people think that Christianity is just about being nice, and it's not. Christianity, at its core is about Jesus Christ taking on God's wrath on the cross as the only means for us to be reconciled with God. Certain aspects of being kind and compassionate do cross over with other faiths but the central tenant does not.
Some people interpret the Gospel through a universalist or cynical lens and reject the notion that Jesus is the only way, and cite their own research as reason for believing what they do. However, this goes against orthodox Christian theology. There are a vast amount of Christian denominations but they do all generally agree on Christ's atonement for sin (and us as inherently sinful) as the core of Christianity.
I have had conversations with people who vehemently claim to be Christian but who reject the Biblical portrayal of Christ. I mean, nobody has to accept the Bible but where are they getting their information about Jesus from if they completely disregard the main text where his teachings are laid out? Who is the Jesus that they believe in, if not the one written about in the Bible? Believe it, don't believe it, that's anyone's choice and prerogative. Absolutely. But if you're going to say you're a Christian, then what do you mean? The Jesus that I follow is the one who was written about in the New Testmant, who was a devout Jew, who believed in the God of the Old Testament (and quoted the OT a lot, showing that he believed it), who went through everything the Gospels describe. He said he was the son of God who came to set us free. Either he was who he said he was in the text where his teachings have been recorded, or he wasn't.
Christianity isnt exclusive in that it is open to anyone who wants it, but once you're in it, it can't be mixed with other faiths. It's like saying you consider yourself a Communist but that you also really like the free market too. Or you consider yourself a vegan as you only eat free range eggs.
I can't speak for Islam as I'm not a Muslim, but Christ in Christianity is vastly different to the Jesus of the Qu'ran. They aren't the same Jesus.