Jesus fulfilled the sacrificial requirements of the Law, which was given the nation of Israel, not gentile nations. As Christian's we are adopted into the line of Abraham and the Bible then become our guide as to what God considers sin or unacceptable behavior. The New Covenant (Testament) is just that a New Covenant God made with mankind through Jesus Christ.
Now back to the Greeks. Sparta artificially separated the sexes at age 7 when the boys started their military training. At age 14 these boys were assigned an older mentor whose age was usually about 21-25. This arrangement was to foster a kinship that served Sparta well on the battlefield. Spartan men were required to marry at age 30 and produce offspring, however, they were not allowed to live with their wives who were chosen for them. In fact in order to consummate the marriage the men had to sneak out of their barracks and then sneak back in. If they were caught they could be severely reprimanded. A Spartan citizen did not live with his wife until after he retired from the army.
What we consider sodomy was also illegal for Greek and Roman citizens. Such activity was limited to boys and men kept as sex slaves. In most cases this would not have been consensual on the part of the slave. The only Roman Emperor to attempt to live an out and proud gay life was Tiberius, which so enraged the Senate and Roman citizens he took a trip with his lover who mysteriously died. Tiberius then retired to Capri and from public life. It is rumored Tiberius had his lover assassinated to calm the Roman citizenry and Senate.
You can quote Plato all you want; there are other Greek philosophers who disagreed with him and did not look upon homosexuality as moral or acceptable.