Ugh. This is the problem with these things - the host thinks it is such a great idea to marshall all the friends and relatives, and it becomes a contest of who can be the most nobel. In my view, it's not as if the child understands all of this, and it forces people to give to a charity they might not support otherwise. A lot of people, for example, love the Red Cross, and others feel that the chief exec makes way too much money and too much goes into overhead. At least until there's a disaster and the Red Cross is needed.
But you're right - it's no one's business!!! It's rude of the host family to put the guests in this position. I also feel there's a certain amount of unstated pressure to give even if you don't attend the party. That doesn't happen with regular birthday gifts.
If they TRULY want to support the Red Cross, they will be grateful for every contribution, whether it's on the thermometer or not. Send a check for a small amount, and staple a note to it that you want the gift acknowledged to the family but NOT the amount. If you say this is your final donation to them if they disclose the amount, they'll listen. My mother gives to charities and tells them this gift is what they are getting for the year, and if they inundate her with mailings or phone calls, she won't give again in the future. It works 95% of the time.
Either that, or stay home from the party.
I think, if the guest wants to support a cause, one way to do it is to purchase something from an organization that the child would like - a gift from a museum store, for example, or a magazine from an organization that's on a subject of interest to the child (wildlife magazine from the World Wildlife Fund, for example). But in that case it's the choice of the gift giver, not the family receiving it.
But that's just me. And I'm with you!!