Are there Drupal modules that help process e-mails dynamically I had the idea of implementing a workflow module for e-mail communications, something like this:

User role 1 can write e-mails (as nodes or custom entities)
User role 2 can review and approve e-mails
User role 3 can press send

I would then like the website to catch replies and enter them into the database with reference to the user entities that touched the e-mail entity, so that the workflow can also be applied to replies.
The part that I'm not sure I can do here, is doing advanced e-mail processing based on which users touched the e-mail.

Are there any modules that can handle encoding these entity references into the reply-to or message of the e-mail so that the Drupal site can process the replies dynamically?
Inmail is designed to be the low level framework to receive mails within Drupal. We proposed in D8 to also implement Mailhandler on top of Inmail and there's good chance this will happen to reduce complexity.

Inmail "works" and you can write plugins to handle the mails.

What you need is a system that supports dynamic mail addresses (through e.g. address expansion). They then need to be redirected / forwarded to the site. This is more a mail server (MTA) configuration than inmail on its own. Through this, every reply is sent to a unique mail address (defined when sending). You can then while handling the mail easily lookup the reference / know the origin.

We plan to add more support for common mail configuration to consider these dynamic situations through configuration only at some point.

Check the issue queue, open feature requests if you can't find a proper issue and start contributing to it! ;-)