Oddly enough, I found two workarounds that worked for me.
1st, Disable "Advanced Security" in my Eero router firewall. This is not my favorite, as I don't like disabling security to make a product work. Noted the domain names/IP addresses that ccleaner64 communicates with, but they seem to be connecting to a range, or at lease a few different remote endpoints. Having the list of domains to whitelist, this would be better.
2nd, Connect to VPN. When I connected to my PIA VPN, ccleaner was able to connect. This is the workaround that I will likely use until ccleaner provides a list of domains that need to be allowed.