hello
I have the same problem
when I config apache<-varnish<-nginx with php-fpm the website go down (with php-cgi it's ok)
finaly I try two things and now it's working (but I don't know why)
1) in "user accounts -> fix permissions" for user nobody, I fix permissions from 644 to 755 php files (maybe it's not that)
2) I think it's that, after compil all php-fpm in "php setting -> php selector 2" and also "php setting -> php-fpm selector" I compil the php x.x.x
and go back to "webserver setting -> select webserver" check about the good php-fpm for apache and nginx (select the version on down) and select "only apache
click on save & rebuild, check if your website go back, if ok, use a terminal with a "top" command and go back to click on your website to make the user working, here you can see if the user use php-cgi or php-fpm
let's go back to nginx->varnish->apache->php-fpm (check again with "top" command and clicks on your website, if it's all right) you have the best config
if that help you, a thank is good, if you find something else or the "why", say it here
hope that help you