According to Swing tutorial:
Some Swing component methods are labelled \"thread safe\" in the API specification; these can be safely invoked from any
Google taught me that at least those are threadsafe. Here's an overview for the case that the link get broken again:
replaceSelection()
insertComponent()
insertIcon()
setLogicalStyle()
setCharacterAttributes()
setParagraphAttributes()
insert()
append()
replaceRange()
replaceSelection()
setText()
print()
getPrintable()
insert()
setLogicalStyle()
setCharacterAttributes()
setParagraphAttributes()
addAttribute()
addAttributes()
removeAttribute()
removeAttributes()
reclaim()
render()
remove()
insertString()
createPosition()
insertString()
setParagraphAttributes()