The last time I set up Graylog I had to configured SELinux.
Allow the web server to access the network:
sudo setsebool -P httpd_can_network_connect 1
Graylog REST API and web interface:
sudo semanage port -a -t http_port_t -p tcp 9000
Elasticsearch (only if the HTTP API is being used):
sudo semanage port -a -t http_port_t -p tcp 9200
Allow using MongoDB default port (27017/tcp):
sudo semanage port -a -t mongod_port_t -p tcp 27017