The Linux community works very hard to keep their operating system and packaged software spyware free. You should not be finding any spyware in bundled linux distributions - if you do you should report it to that distro and to linux.org.

The spyware tends to come more from visiting malicious websites, applications that require you to install browser toolbars in order to run, certain free game sites or free calendar applications that require you to install activex components.

Also I must clarify for you - Fedora is Not Red Hat Enterprise. Fedora is a completely separately managed and coded Free distribution run by Red Hat. Red Hat used to release their distro under the name Red Hat and it was a general mainstream all purpose distribution. They decided it would be best to separate the server tasks from desktop tasks. Red Hat Enterprise is from the ground up coded as a server. Fedora from the ground up is coded as a mainstream desktop.