Interpreting "毛主席是我们心中的红太阳。" (Chairman Mao is the red sun in our heart)
This sentence compares Chairman Mao to the sun. We all know how great and important the sun is. It gives us light, it gives us warm and it gives us hope; Without it, there will only be darkness, cold, and hopelessness. The sun is the object to be worshipped.
This sentence (slogan) is expressing how much the Chinese people are worshipping Chairman Mao. It is a part of the movement to deify Chairman Mao at the time.
And why a red sun? Because the color of the Communist Party is red, (implies Chairman Mao is the sun for Communism)
As for how 太阳 was translated as 'fucker' on the sign, please read Mo.'s answer to this question.
There's a theory that goes something like: 紅太陽 = 紅日 = red fuck. But, that seems a bit preposterous to me.
This is on purpose, the translator is a troll