User m-watson's comment made me look up if any B Corps have gone public and there certainly are IPOs. [1] Including subsidiaries of majors like Coca Cola. The few I looked up listed on NASDAQ and had overall flat performance. Which I guess is what you would expect?

Disclaimer: I am an investment neophyte, would love to be corrected or expanded upon.

[1] https://kb.bimpactassessment.net/en/support/solutions/articl...

If you are talking about for profit benefit corporations (B-Corps), they can IPO. They are essentially just C-Corps with non-financial tracking metrics written into the bylaws.