At least if your org is on Office365 and doesn't have too restrictive policies, you can get your email over standard IMAP. There also exist some nice man-in-the-middle proxies which pretend to exchange servers that you've implemented the policies they ask for.

I've got multiple "work" (one is a volunteering role) office365 exchange accounts on my personal phone, using [https://sites.google.com/site/bikomobi/exchained](exchained). Seems to work well. I'm sure the respective IT departments would give me a stern talking to, but there is nothing in either job that is of any sensitive nature whatsoever so their blanket "ask for admin permissions on my phone" policies can get fd, frankly.