Craigslist has a nice feature where when you respond to a poster you respond to an email such as job-fepsd-1120347193@craigslist.org. The email is then in turn direct
Elastic Email has a simple API for creating two-way anonymous email routing just like craigslist or airbnb. It uses an inbound email api to call a web-hook on your server to resolve the correct email addresses and then relays the email accordingly. It only takes a few lines of code. They have a detailed tutorial here:
https://elasticemail.com/blog/marketing_tips/how-to-build-an-anonymized-email-relaying-feature-using-elastic-email/