Biden has not been socially liberal. He’s been an establishment Democrat his whole career. He has trailed the left and towed the line of the party, but he has patently not been socially liberal. However, he has atleast brought on policy advisors who are socially liberal like Heather Boushey, Stef Feldman, and Brian Deese.
Here are some links for reference.
https://www.nytimes.com/2023/03/09/us/politics/biden-centrist.html
https://www.cnn.com/2021/04/11/opinions/biden-budget-proposal-centrism-ghitis/index.html
https://www.nytimes.com/2020/10/29/us/politics/joe-biden-advisers.html
If you drop the paywall link into archive.is you’ll get an archived version back.
https://archive.is/hSboX
If you can afford it, please donate to the EFF, Internet Archive and the New Republic.
https://supporters.eff.org/donate/join-4--s
https://archive.org/donate/
https://newrepublic.com/