Help me do my washing

Python 3, 37 bytes

lambda a:[[c]*a.count(c)for c in"LD"]

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APL, 8 bytes

'DL'~⍨¨⊂

Explanation:

• ⊂: enclosed input
• ~⍨¨: without each
• 'DL': 'D' and 'L'

Examples:

      ('DL'~⍨¨⊂) 'LDLDD'
┌──┬───┐
│LL│DDD│
└──┴───┘
      ('DL'~⍨¨⊂) 'LLL'
┌───┬┐
│LLL││
└───┴┘
      ('DL'~⍨¨⊂) 'DD'
┌┬──┐
││DD│
└┴──┘
      ('DL'~⍨¨⊂) ''
┌┬┐
│││
└┴┘

Haskell, 28 bytes

f l=[filter(==[c])l|c<-"LD"]

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If the input can be a list of characters, the [] around c can be removed.