If something transforms your life in a positive way then by all means, I would recommend pursuing it. When I say positive, I'm also referring to common ideas such as life, love, joy etc.
Are there things that have improved your life that you wouldn't recommend backing? Ponders your response*
Typically people have freedom to believe or not believe, unless they live in Iraq. But yes, of course there are people who are christian in name only. And of course if someone follows a faith that hurts them in some way, they're free to separate from it, and I'm sure id do the same.
While I think following a faith is fine, I don't think people being forced to follow a religion is fine, if this is your concern.
Often times missionaries help those who request help. Missionary work comes in all shapes and sizes. I wouldn't consider it disruption at all to build houses for impoverished children, not in a negative sense at least. And if they convert as a product of that, or even further are taught how to build their own houses and go and build for others, I think it would be hard to downplay these benefits.
Some missionaries I would agree though, go on irrational missions, such as the guy who visited that south American tribe who risked receiving diseases from the missionary that would have killed them, and they shot the missionary with a bow and arrow and he died as a result.
These kinds of missions, I would absolutely agree are negatively disruptive and I can't imagine I'd ever partake in. But these don't really change the more common case such as the one described above. Which seem worthy of support to me. But ultimately the goal is to love on others and to show others the love of Christ.That ought to be the root of the equation. Jesus gave us everything, the least we can do is give you a roof to sleep under.
Non religious ideas make no claim of unique correctness?

tell that to Dawkins.
People are free to believe what they want, even as a Christian. But that doesn't mean that you have to go out calling the world wrong, same with atheism. Though some people choose to call others wrong, oftentimes in a distasteful way. Though this does go both ways.
I never said other faiths (or non faiths) that have transformed other's lives in a positive way must be wrong. Or at the least, not a wrong choice for them to follow.
And as I've said multiple times before, people don't trust in Christ because they have scientific proof of the trinity. I agree that no Christian is going to be in a position to demonstrate that the Christian way is the "true path", but I don't think that should stop people from getting behind something that they see has transformative power in ways that help them or others around them.
If you like red sauce on your pizza, pick the red sauce. If someone else likes white sauce, that's fine, good for them. You don't have to agree nor do you have to scientifically know which sauce is truly the best to support one or the other. And if the red sauce burns your tongue, then by all means, you can walk away from the red sauce and can try bbq. I would do the same.
But if a sauce is good and you experience it's benefits, seems rational to me to get behind it.
There's a book Ive read, written by a pastor, on the extent of Christ's love, even for non-christians. You might be interested in hearing about it or at least it's ideas on these kinds of topics. Maybe when I have more time, I can share. Imagine a case where a black slave has a white christian slave owner. He slave views the Christian faith as a terrible thing because she has learned it through an abusive master. She walks away from Christ. Even in these scenarios, it's feasible that Christ, so loving the world, would even seek to save this individual, even if they died as a non Christian. It's not up to man to decide who goes to heaven or who doesn't, nor would Christ want people to force one another into religions that oftentimes more than not, misrepresent his will for us. And personally I don't think Jesus would support missions trips that negatively impact a societies ability to survive. Even if you love those south Americans, if you bring diseases to them or they shoot arrows at you, you're probably doing something wrong with your mission and likely aren't carrying out Christ's will if you're risking everyone's well being for your own selfish feel-good objectives.