Can a person be Christian and also agree that all other world religions are valid? Or do I have to ignore, condemn and refuse to have anything to do with them?
No, one cannot be a Christian without rejecting all other world religions, and recognizing them as sure paths to condemnation. The Bible is the word of God, and if you believe in Jesus Christ then you should treat his word with the appropriate respect, should you not? The Bible addresses all of these issues:
Whoever believes in the Son has eternal life; whoever does not obey the Son shall not see life, but the wrath of God remains on him. (John 3:36)
The Bible teaches that non-Christians will go to hell. We are commanded to love and pray for non-Christians, but we cannot respect their personal beliefs. Non-Christians, whether they be Jews, Muslims, Hindus, Buddhists, or pagans, are worshiping false gods and will go to hell for doing so unless they receive Jesus Christ. This is because all humans are fallen sinners, and are redeemed only through faith in Jesus Christ. To say that non-Christians can be saved is to deny inherent human sinfulness. The Bible is clear that Jesus' death is only effectual for those who call on his name,
But to all who did receive him, who believed in his name, he gave the right to become children of God, who were born, not of blood nor of the will of the flesh nor of the will of man, but of God. (John 1:12-13)
The Bible says that those who do not believe in Jesus Christ cannot know God through any other religion,
Everyone who goes on ahead and does not abide in the teaching of Christ, does not have God. Whoever abides in the teaching has both the Father and the Son. (2 John 1:9)
So, it can be shown that one cannot be a Christian and believe that non-Christians will go to heaven. But what about participation in false religions? The Bible speaks on this too. The Apostles of Jesus Christ sent letters to the non-Jewish churches instructing them to avoid the idol sacrifices of the Greeks and Romans,
But as for the Gentiles who have believed, we have sent a letter with our judgment that they should abstain from what has been sacrificed to idols, and from blood, and from what has been strangled, and from sexual immorality. (Acts 21:25)
Paul instructed the believers in Corinth to stay away from the false Greek religion of the time,
What do I imply then? That food offered to idols is anything, or that an idol is anything? No, I imply that what pagans sacrifice they offer to demons and not to God. I do not want you to be participants with demons. You cannot drink the cup of the Lord and the cup of demons. You cannot partake of the table of the Lord and the table of demons. (1 Corinthians 10:19-21)
Indeed, you cannot participate in both the Lord's Kingdom and the pagan kingdom of Satan. To practice paganism is tantamount to serving the devil, and one cannot serve the Lord Jesus and his enemy at the same time.
Now as to respecting false religions, the Bible also precludes this possibility. You should certainly respect people who practice false religions. Indeed we are commanded to do more than mere respect: we must love these people. But we cannot respect what they believe. The Bible has nothing but mockery for false, non-Christian religions,
To whom then will you liken God, or what likeness compare with him? An idol! A craftsman casts it, and a goldsmith overlays it with gold and casts for it silver chains. He who is too impoverished for an offering chooses wood that will not rot; he seeks out a skillful craftsman to set up an idol that will not move. Do you not know? Do you not hear? Has it not been told you from the beginning? Have you not understood from the foundations of the earth? (Isaiah 40:18-21)
I am the LORD; that is my name; my glory I give to no other, nor my praise to carved idols. (Isaiah 42:8)
All who fashion idols are nothing, and the things they delight in do not profit. Their witnesses neither see nor know, that they may be put to shame. (Isaiah 44:9)
The carpenter stretches a line; he marks it out with a pencil. He shapes it with planes and marks it with a compass. He shapes it into the figure of a man, with the beauty of a man, to dwell in a house. He cuts down cedars, or he chooses a cypress tree or an oak and lets it grow strong among the trees of the forest. He plants a cedar and the rain nourishes it. Then it becomes fuel for a man. He takes a part of it and warms himself; he kindles a fire and bakes bread. Also he makes a god and worships it; he makes it an idol and falls down before it. Half of it he burns in the fire. Over the half he eats meat; he roasts it and is satisfied. Also he warms himself and says, "Aha, I am warm, I have seen the fire!" And the rest of it he makes into a god, his idol, and falls down to it and worships it. He prays to it and says, "Deliver me, for you are my god!" They know not, nor do they discern, for he has shut their eyes, so that they cannot see, and their hearts, so that they cannot understand. No one considers, nor is there knowledge or discernment to say, "Half of it I burned in the fire; I also baked bread on its coals; I roasted meat and have eaten. And shall I make the rest of it an abomination? Shall I fall down before a block of wood?" He feeds on ashes; a deluded heart has led him astray, and he cannot deliver himself or say, "Is there not a lie in my right hand?" (Isaiah 44:13-20)
Who is the liar but he who denies that Jesus is the Christ? This is the antichrist, he who denies the Father and the Son. (1 John 2:22)
We can see that in the Bible, God makes fun of other religions and ridicules them as worthless. And I would join Jeremiah in asking you, "Can man make for himself gods? Such are not gods!" (Jeremiah 16:20). God does not merely declare false religion as false, he refers to it as outright idiocy. How then can we respect what our Lord has mocked? No, there is no true religion in the universe that rejects Jesus Christ, and we thus cannot have anything but contempt for other religions. This should motivate us even more to love those who are lost in such ridiculous faiths. But we certainly may not partake with them in this folly.
Anyway, I hope this helps to address your questions.