They don't ignore the thousands of children who die every day. You might not know about it, but Christians support all kinds of charities: food kitchens, medical missions overseas, operation christmas child which gives gifts to kids, the international justice mission which seeks to break kids and adults out of slavery... There are hundreds of examples.
One closely related to the topic at hand: crisis pregnancy centers often supply help to new mothers in addition to counseling them to no seek an abortion. That could mean short term housing, job training, community support (bible studies with other mothers), diapers and other baby supplies, etc...
Just because you can't help everyone doesn't mean you shouldn't
try to help someone.
You know it would be really great if Christians support all of the things you mentioned without resorting to conversions. There shouldn't be any ulterior motive attached to goodwill. Else it can no longer be called charity and should be labelled trade. What Christians really need to do (especially those in the West) is check if the money and clothes that they donate to Missionaries are actually being used honourably. The end goal should not be soul harvesting at the expense of someone's misery. Genuine goodwill will never go unappreciated; mix in religion and the Act loses it's benevolence. Sorry to put it so bluntly.
One closely related to the topic at hand: crisis pregnancy centers often supply help to new mothers in addition to counseling them to no seek an abortion. That could mean short term housing, job training, community support (bible studies with other mothers), diapers and other baby supplies, etc...
Just because you can't help everyone doesn't mean you shouldn't try to help someone.
How is any of that hypocrisy?