As you noticed in reply to TimS below, the out is heavily weighted toward religious objections. That's partly the result of religion's privileged position in society, but also because they expect pacifism to be the output of some philosophy you hold, not your philosophy itself.
So, even if you have a long history of anti-war donations, the draft board is going to need to hear some Theory of Everything that has pacifism as a derivable theorem, not an axiom.
Do you think it's wise to only give them some Theory of Everything? That is, can I push down Pr(conscription) by thinking hard about how to describe my Theory of Everything and giving visible signs that I actually believe it. It just seems awfully risky, especially being an atheist, to rely solely on hoping my impassioned account of my views will convince them alone. Sure, donations or other pacifist actions might not help much if I can't give a Theory of Everything. But that same deficiency might apply in reverse too.
Suppose that you believe larger scale wars than current US military campaigns are looming in the next decade or two (this may be highly improbable, but let's condition on it for the moment). If you thought further that a military draft or other forms of conscription might be used, and you wanted to avoid military service if that situation arose, what steps should you take now to give yourself a high likelihood of being declared a conscientious objector?
I don't have numbers to back any of this up, but I am in the process of compiling them. My general thought is to break down the problem like so: Pr(serious injury or death | conscription) * Pr(conscription | my conscientious objector behavior & geopolitical conditions ripe for war) * Pr(geopolitical conditions ripe for war), assuming some conscientious objector behavior (or mixture distribution over several behaviors).
If I feel that Pr(serious injury or death | conscription) and Pr(geopolitical conditions ripe for war) are sufficiently high, then I might be motivated to pay some costs in order to drive Pr(conscription | my conscientious objector behavior) very low.
There's a funny bit in the American version of the show The Office where the manager, Michael, is concerned about his large credit card debt. The accountant, Oscar, mentions that declaring bankruptcy is an option, and so Michael walks out into the main office area and yells, "I DECLARE BANKRUPTCY!"
In a similar vein, I don't think that draft boards will accept the "excuse" that a given person has "merely" frequently expressed pacifist views. So if someone wants to robustly signal that she or he is a conscientious objector, what to do? In my ~30 minutes of searching, I've found a few organizations that, on first glance, look worthy of further investigation and perhaps regular donations.
Here are the few I've focused on most:
Center on Conscience and War
Coffee Strong
War-Resister's International
The problems I'm thinking about along these lines include:
I'm curious if others have thought about this. Good literature references are welcome. My plan is to compile statistics that let me make reasonable estimates of the different conditional probabilities.
Addendum
Several people seem very concerned with the signal faker aspect of this question. I don't understand the preoccupation with this and feel tired of trying to justify the question to people who only care about the signal faker aspect. So I'll just add this copy of one of my comments from below. Hopefully this gives some additional perspective, though I don't expect it to change anyone's mind. I still stand by the post as-is: it's asking about a conditional question based on sincere belief. Even if the answer would be of interest to fakers too, that alone doesn't make that explanation more likely and even if that explanation was more likely it doesn't make the question unworthy of thoughtful answers.
Here's the promised comment:
Stated another way: