Google taught me that at least those are threadsafe. Here’s an overview for the case that the link get broken again:
JTextPane
replaceSelection()
insertComponent()
insertIcon()
setLogicalStyle()
setCharacterAttributes()
setParagraphAttributes()
JTextArea
insert()
append()
replaceRange()
JTextComponent
replaceSelection()
setText()
print()
getPrintable()
UndoManager
- All methods.
DefaultStyledDocument
insert()
setLogicalStyle()
setCharacterAttributes()
setParagraphAttributes()
StyleContext
addAttribute()
addAttributes()
removeAttribute()
removeAttributes()
reclaim()
AbstractDocument
render()
remove()
insertString()
createPosition()
PlainDocument
insertString()
HTMLDocument
setParagraphAttributes()