A few things...
1. Statues, or any artistic depictions, of God are not necessarily idols, certainly not
false idols, as God is a real god not a false one (according to the Christians who built this at least). The wording of the idolatry commandment clearly aims at idols of things other than God to replace Him, which includes Earthly animals but also Heavenly things like angels which people in the Bible would sometimes make the mistake of worshiping.
It is ambiguous as to the depiction of God Himself, which would also be Jesus to most Christians. It should be acknowledged that among all of Jewish history there has almost never been a statue depiction of God, but Jews have more scriptures than just the Tanakh (the Christian Old Testament) that may be more explicit than the Commandment. The same could be said of Islam. But both of those religions have had periods of history where
drawing or painting God was acceptable, and pictures have a relation to idols.
Christians started making statues of Jesus, but it's on a different level since for Christians God has a physical incarnation they can make a statue of. If no one has ever seen God Himself in his Heavenly form (and no one has according to Christians), then you can't make a statue of something you've never seen. I'm sure another part of the reason Christians are okay with statues is from the artistic inheritance of SPQR as well, but the main "excuse" would be that unlike Jews or Muslims, Christians have seen God in physical form and can therefore depict Him.
2. Jesus was a Jew and more than likely looked like any other Jew for his time and place, which means he wasn't white or black, but probably had a tanned olive complexion with a large nose and curly hair (could be black or red). Since there isn't a record of what he specifically looked like, artists used hearsay for some features and made the rest in their own race's image. Think about it, if you're a medieval Italian, you've probably never seen a middle-easterner in your life, and you've probably never read the whole Bible (if you read at all) to understand He was a Jew. A lot of medieval and renaissance paintings will also depict clothing and architecture as from their own culture rather than ~1 AD Judea for the same reason.
One feature that's popular in His depiction is long hair, which some scholars believe to be due to a misunderstanding. He was from Nazareth, a town, which made him a Nazarene, like how being from Chicago makes one a Chicagoan. There was a voluntary religious order among the Jews called the Nazerites who would not cut their hair and not drink wine in order to get closer to God. Samson was a famous Nazerite. So that may be a reason he's always shown with long hair.