I'm not sure about the translation, but I think that would be this:
After bearing A's thoughts, the action, which B found there and took, is....
思い=thoughts
受け=to bear or receive
応援してくれるひとたちの思いを受けて、政治家として立候補する。
Bearing my supporters' thoughts, I will stand as a candidate for a politician.
I don't think this is a good translation, but I would be happy if this will help you any.