I've seen this before. It occured only when the customer was logged in as administrator and viewed their own site. We tracked it down to the site running out of memory. What happened was the site had several plugins installed already and installing Wordfence pushed the site over the memory threshold, but only when the admin was logged in because that consumed slightly more memory for some reason.
So when a page loaded, the site blank screened and wrote an out of memory error the the error log.
There are several fixes you can try:
1. Ask your host to increase the allowed memory in php.ini
2. Ask your host to increase the Apache memory limit specified in Apache config with the parameter RLimitMem.
3. Make sure there are no "killed daemons" running on the machine that kill processes that consume too much memory.
4. Remove memory hungry plugins to reduce your memory usage. I wouldn't recommend this because I'm finding that many "cheap" hosts are simply not allocating enough memory for a modern WordPress installation these days. So first tell them to give you what you paid for.
Hope that helps. Let me know if you see anything in your error log that indicates it's not memory, but I'm pretty sure that's what it is.