Weirder or less weird about this than about other things people do with their money?  Seems better than going on vacation or owning fancier houses, which are things nobody bats an eye at.

Is the conflict about how much social credit you give the donors for being generous, but inefficient?  You want to appreciate the generosity while bemoaning the inefficiency. Sounds like you are, at least a bit, Utilitarian in that.

I personally focus on the generosity - doing something uncoerced to help someone, at some cost to oneself, is laudable.  Yay them!   There are certainly some ineffeciencies and side-effects that would make the consequences negative or zero, and this would make me less supportive, of course.  But that doesn't apply here - I recognize that it's complicated what the actual effects are.  The $2M isn't being burned to keep the kid alive, it's going to fund professionals, equipment, and systems which will save the kid, but also be in place to save more kids and generally get better at saving people.

It's worth noting here that 2 million USD is less then the price that economists usually use to decide whether policies that save first-world lives are desirable where a consensus number for a life is around 7 million USD. 

It's easier to save third-world lives then that but there's a lot of things compared to which saving third-world lives seems more effective. 

Well, there is chance that a part of your brain tries to answer "how much is a stranger's kid's life worth?" and returns a number between $50K and $2M. The specific number is censored from the rest of your brain, because thinking of any specific number would make you feel bad.

Thinking about smaller numbers makes you feel "definitely worth it", to which the PR module of your brain attaches "because human life is sacred". Thinking about larger numbers makes you feel "nope", and the PR module searches for a plausible excuse (such as "this is probably a scam"). In both cases, the PR module tries to deny that the actual decision method was comparing two numbers.

However, you are smart enough to realize that all excuses against $2M apply also to $50K. It would be nice if an external authority could tell you what is the correct number, but you are familiar with effective altruism and believe that for $50K you could save more than one life. So you cannot use this specific authority to support your feelings.

I would guess that with small differences in budjet there could be doubt whether all the money goes into saving. With a big budjet redirected to smaller projects even if the small projects would be top 10% inefficient in the saving in money they would probably be more saved lifes. Not being able to name the factors that delineate whether or not to redirect is probably the source of the funny feelings. Even if people argue and had different opinons of where the line goes if everybody firmly understands their own stance such feelings don't arise. Like the saying "if it is too good to be true it probably isn't" this is a scenario of "if it is too insistent then it is a chooser rather than a begger "