Hi, can you run pihole -d and get us the token so we can take a look. I just ran through an install on a Centos 7.3.1161 and confirmed that the permissions are correct and the user is right. The debug log should show us some more information though.
This circumvents the issue you are seeing as it prevents dnsmasq from trying to access the log file. Unfortunately, this means that logging is now disabled.
By any chance, do you use SELinux on this machine?
Okay, we do have a warning on install for some recent releases that notes for SELinux enabled systems you would need to set the confinements for files in order to work properly. It's possible to run with SELinux in a degraded security mode, but it's not suggested.
In order to run with SEL enabled, you would need to set the rules on your system to allow dnsmasq to access that file.
Once you have the constraints set on that file, then it should start up with no problems. Since it's modifying the security of the operating system, we decided a few releases back to just warn the user and let them modify if they chose, instead of installing a custom security policy. If we can be of assistance, let us know, however the latest policy that we have needs to be tuned and cleaned up, it was a little too permissive for our likes.
I've done my initial bit of getting PiHole up and running against Fedora29. I'm not entirely happy as this gives way to much power to the httpd process - in a next iteration I'm going to add some custom types to limit this power.