I've run my own mail and web servers from my home for years, so I was worried about this when I was making the switch from Time-Warner cable (who didn't care, BTW) to Verizon Fios. One person I know reported that Verizon did indeed block port 25 (and port 80) inbound, while another told me his setup worked fine, once he replaced the free router they gave him with his own router.
And indeed, after making the switch, I still am able to get mail inbound on port 25. The modem/router they gave me does have controls to adjust security settings, which look a lot like Windows trusted -vs- untrusted controls. But I can't really tell if they do much. The key thing I found was to set up port forwarding to send port 25 to the machine in my internal network with the mail server. Same for port 80 to the web server.
Outbound I route through the ISP. Postfix makes that easy. I found a few years ago that certain domains I sent to, though not all of them, started bouncing mail even though I had an SPF record, just because my IP address was in a range listed as "dynamic" (i.e. "residential"). Clearly that's for spam control. Not everybody does this, and I could send direct to those who do not, but it was simpler to just send everything out via port 587 to the ISP.