Google is a company. They should not be taking political sides to begin with. However, if they do choose a side, they should agree with the platform. If there is something the company feels strongly about, they have the right to pull their support. Everyone should make decisions to support/not support political groups based on the facts.
If Google believed that the group was lying than they were right to pull out. It would look very bad on them if they went ahead with it and then it was found out the group was lying. I think that the did the right thing because this is a very important issue.
Google is a business and they can make business decisions however they see fit. If they want to pull their funding from a political figure because of something they don't agree with then they have the right to do that. We shouldn't judge their beliefs on anything and they can do what they wan with their money.
Google is known as a warehouse of knowledge throughout the world. If they continued to support a climate change denying political group, they would undermine their position as a progressive company. Legitimate scientists have agreed for years that human beings are responsible for the latest climate changes. Google would seem stuck in the stone age if they sided with the science deniers.