I noticed a number of discussions here and elsewhere about rooted phones having a sync notification that won't go away. After some testing I've been able to replicate and fix the problems that cause this little nuisance.
The issue lies in the fact that account sync information is not tied to the application files themselves. In other words, if you remove HtcTwitter.apk from your phone but have a Twitter account setup in 'Settings > Accounts & Sync,' you will get a persistent sync indicator as the phone tries to update that account using software it can't find. If you don't have a Twitter account listed you can safely remove the application files from the phone without getting the persistent sync indicator.
The biggest culprit is Friend Stream. If you have a Facebook, Twitter, or Flickr account setup in 'Settings > Accounts & Sync' you will not be able to remove Friend Stream without getting the persistent sync indicator. However, if you remove those accounts from the phone, THEN remove Friend Stream, the sync error will go away.
It appears that the Friend Stream software is integrated into other phone software; like, pulling Flickr and Facebook photos into the Photo apps, or pulling Facebook status updates into the phone contacts. So, if you plan on using the built in Facebook contact or Facebook/Flickr photo integration you'll need to keep Friend Stream - otherwise you will end up with the persistent sync indicator.
(TL;DR: Remove Facebook/Twitter/Flickr accounts from 'Settings > Accounts & Sync' before removing related software. Don't remove Friend Stream unless you aren't going to use the integrated Facebook and Flickr features.)
The issue lies in the fact that account sync information is not tied to the application files themselves. In other words, if you remove HtcTwitter.apk from your phone but have a Twitter account setup in 'Settings > Accounts & Sync,' you will get a persistent sync indicator as the phone tries to update that account using software it can't find. If you don't have a Twitter account listed you can safely remove the application files from the phone without getting the persistent sync indicator.
The biggest culprit is Friend Stream. If you have a Facebook, Twitter, or Flickr account setup in 'Settings > Accounts & Sync' you will not be able to remove Friend Stream without getting the persistent sync indicator. However, if you remove those accounts from the phone, THEN remove Friend Stream, the sync error will go away.
It appears that the Friend Stream software is integrated into other phone software; like, pulling Flickr and Facebook photos into the Photo apps, or pulling Facebook status updates into the phone contacts. So, if you plan on using the built in Facebook contact or Facebook/Flickr photo integration you'll need to keep Friend Stream - otherwise you will end up with the persistent sync indicator.
(TL;DR: Remove Facebook/Twitter/Flickr accounts from 'Settings > Accounts & Sync' before removing related software. Don't remove Friend Stream unless you aren't going to use the integrated Facebook and Flickr features.)