It appears to be impossible to prevent the beagle search window from
popping up at the beginning of every session (short of doing an
"rpm -e beagle" command :-).

The other apps that auto start generally seem to let you right click
on the taskbar icon, select "quit", then popup a dialog box to ask
it you want to autostart on login.

Beagle needs the same thing the other apps have. There are a lot
of old fuddy-duddies out there like me who hate "helpful" apps. No
matter how proud you are of beagle, some of us would like it to
disappear :-).