It is an issur d’oraysah. Reb Moshe, in the Igros Moshe, states that Lo Sikrevu means you can’t talk to girls. Rav Moshe is quoting a statment of Chazal in Avos D’Reb Nosson and rulings of the Ran and others. Avos: “Al tarbeh sichah im haishah” – Do not talk more than necessary with women. The Mishnah continues: “Whoever does talk more than necessary with women causes bad for himself . . . and in the end will end up in Gehinnom!” Re derech chibah: The Halachah (Rambam) prohibits negiyah even in a non-affectionate manner. Casual negiyah is also prohibited — see the Steipler’s Letters quoting the Chazon Ish for details — even if it doesn’t “mean anything”. Even regarding a simple handshake between strangers, Rav Moshe writes that you should not rely on this as a heter.
Lo Sikrevu – the Torah prohibition of touching – is referring even to non-affectionate touching, according to the Rambam. The Ramban argues, and holds that non-affectionate touching is not included in the possuk, but is assur nonetheless m’drabbanan. The prohibition of Lo Sikravu applies to all ages equally. There is no logic in saying that an explicit Torah prohibition is “not talking” about certain ages.
Shulchan Aruch Even HaEzer:
“A person must stay far, far away from the women, and it is prohibited to signal with your hand, to hint with your eyes, to any prohibited women. It is furthermore prohibited to laugh together with them and to be frivolous in her presence, or to watch her beauty. Even to smell her perfume is forbidden….”
Rav Moshe addressed the Derech Chibah issue in his Teshuva, saying that whenever boys and girls are friends, even innocently, that is considered Assur, like Derech Chibah. R. Moshe Feinstein repeatedly (Iggeros Moshe, Orach Chaim vol. 1 no. 113; Even Ha-Ezer vol. 1 no. 56) ruled that a man enjoys shaking a woman’s hand and it is therefore
prohibited. The Steipler writes in his letters in the name of the Chazon Ish that it is absolutely prohibited. Regarding a so-called heter that you will embarass her if you don’t shake hands, it’s simple logic: If someone asked you to call them on Shabbos and you telligng them sorry I cant do that would embarrass them for asking, would you be mechalel shabbos to prevent their embarrassment? Or if someone offered you non-kosher food and refusing would embarrass them would you eat treif?