I think this is protected under the constitution, though I could be wrong. This seems to be a freedom in the United States, at least. Elsewhere, I do not know. But, if extremist organizations want to move funds around, if they aren't violent organizations, it must be allowed to take place.
I think that as long as the organization is not actively breaking any laws or is considered a terrorist organization then it is fine to process donations for them, who really determines what organization is extreme or not it's really a matter of opinion and if individuals are willing to donate to them we should allow them to.
I feel that credit card companies should not be allowed to process donations to extremist organizations because doing so is potentially allowing those organizations to take part in violent acts such as acts of terrorism. People that donate money to these organizations are funding groups that are likely to commit violent acts against innocent people.
No, credit card companies should not be allowed to process donations to extremist organizations, because it is a matter of national security. Credit card companies can do a great job stopping terror by making sure they have no resources through this type of donations. This is a small limitation that would do a lot of good.
No, I do not think that we should allow credit card companies that option. It's the equivalent of offering funding to terrorist organizations. In fact, in some cases, that's exactly what it is. You need to shut down the extremists, and the fastest way to that in the 21st century is to cut off their funding.