It is interesting that a historical fact is attacked because of the writer's religion.
The bottom line is, did he die on a cross or a stake, and does that mean something important?
Remember it was Constantine that introduced the cross - almost 300 years after Jesus' death. He said that he had a vision where a cross was in the sky and he heard words "In This Conquer" (in hoc signo vinces). In this way he promoted Christians going to war, which was all right now, he said, because they will put a cross on their shield or on their standard flags.
Constantine was well known for introducing pagan doctrines, practices, and holidays to the churches and bishops who were willing to get his support and temporal power.
What the method of execution that Jesus suffered (as long as he was hung on a tree or stake like the prophecy said) is not quite as important as the introduction of implements and symbols of idolatry into the Christian churches. Idolatry is so evil in God's eyes, that if people engaged in it, God will not allow such a person into the Kingdom of God. 1 Corinthians 6:9-10
Constantine's adoption of pagan doctrines have continued to this day, polluting the worship of many people who don't know that they do that. Most churches have crosses on their steeples. Most churches also have either a picture or a statue of Jesus hanging on and nailed to a cross inside. Many people have crosses as one or more of their pieces of jewelry. Many people even have cross symbols on their Bibles, the same Bible that says "we walk by faith and not by sight" and "little children, flee from idolatry." 2 Corinthians 5:7; 1 John 5:21
But, it is also important to recognize that the word in the Bible that is translated "cross" is not what it says. The Greek word there is stauros, which means stake. That is what the word meant in the first century. There are Greek documents that use the word referring to a simple pole or stake, without a crossbeam. At least the King James Version says "tree" and "stake" in a few places, because where Jesus was nailed fulfilled prophecy. Galatians 3:13 and the original prophecy, at Deuteronomy 21:23, mentioned the stake, also provides the law that says that someone hung that way had to be removed before sundown.
So these are the reasons why people think that Jesus died on a cross People have been taught that since Constantine. Symbols that are shaped like crosses are all over church items, and are told that this which was based on idolatry is a holy thing to do. And people are not told that Jesus was not hung on a cross, but was hung on a stauros, a stake.
We have to listen to the scriptures, in the earliest manuscripts, to get the truth and live by it. Constantine could not save with that cross he said he saw, he couldn't even save the Roman Empire with the cross on his standard.