As far as I am aware there is no cross symbol used in the ancient pagan religions. The closest thing to it would be the ankh from Egyptian paganism, but the ankh is much different than a cross both in how it looks and how it was understood. Also the ancient Egyptians were the most proud race of Ham, so they were not white.
As far as I am aware of the actual history of the cross and the practice of crucifixion, it was indeed made by or at least popularized by the Romans, whom were white. The cross was an execution method, not a symbol, in their pre-Christian understanding, a brutal execution method at that. For example Julius Caesar's start to fame was he was captured by pirates, he promised his captors that he would come back and crucify them when he was released and they mocked and laughed at him. After he was ransomed and released he fulfilled his words and came back and found them and he crucified them.
It is actually quite a testimony against the actual Hebrews of the time that they demanded Jesus to be crucified. They by their own law could not put him to death, so they had the Romans do it for them and demanded the Romans to put him to death in a Roman manner that is not proscribed by the Torah or by Judaism (Oral Torah/Pharisee traditions/doctrines of men.) They even claimed that they had no king except for Caesar, thus they surrendered the authority they claimed to have to Caesar and had their own King crucified without a valid cause. The Romans via Pilate in his temporal authority wrote above Jesus' cross King of the Jews. This means that even though they meant it for sarcastic mockery that the Romans recognized Jesus' divine authority as the King of the Jews. This greatly disturbed the Pharisees whom perceived this because it is a further testament against them that they chose to give their own King, their own Messiah into the hands of the white Gentiles and to have him crucified because they had no faith or belief in their own God. Jesus on the crucifix forgave them saying they know not what they do.
The cross today and shortly after that event has become a symbol, it did not start out as a symbol, but it is one now. The cross is a symbol and a reminder of the crucifixion of Jesus and his forgiveness while on the cross.