Running iptables instead of firewalld cannot be the cause for the issue.
It is correct, that firewalld is the standard for CentOS 7, but it is also correct that on a default setup, CentOS 7 in combination with Plesk does not use firewalld, but is using iptables. You can test whether firewalld is active by asking for the status: # service firewalld status. If it is active, stop it, because iptables will do the work. However, it is probably not even installed on the system.
You can check which version of iptables is installed on your system, e.g.
# rpm -qa | grep iptables
The current version should be iptables-1.4.21-17.el7.x86_64
I do not yet have an idea why an upgrade of iptables causes a full block of the panel and websites, but I assume that for some reason existing rules are being replaced or deleted. It can be that you are not using Epel repository, but some other repository that delivers a ruleset along with the upgrade. I suggest to do this:
1) export existing iptables rules
# iptables-save > iptables-export
2) upgrade iptables through yum
3) import iptables rules from the export file
# iptables-restore < iptables-export