Is CiviCRM compatible with Postgres and Wordpress?
No.

CiviCRM uses MySQL functions extensively, so it can't be run with PostgreSQL.

This has been raised before over on forum.civicrm.org (at least in 2010 and 2007). Tim Otten's answer in this forum post may also help understand some of the workings currently in the DB layer (and specific to MySQL).

It could (in theory) be done, but it would take significant effort and leadership from the community who wanted to make it happen.