Verse 20 is the solution to the problem of verse 19. Since no unclean thing may enter the kingdom of God, we must be clean to enter therein. We care cleansed through baptism in the name of Christ.
Reference: The ultimate reference of the idea nothing unclean can enter the presence of the Lord comes from the brass plates:
2 Chronicles 23:19
19 And he set the porters at the gates of the house of the LORD, that none which was unclean in any thing should enter in.
In Chronicles the context is specifically the temple, not heaven. However, the temple is the house of the Lord because it can (and symbolically always does) house his presence. Thus to enter the temple is to enter the presence of the Lord (on earth). If we cannot enter therein in an unclean state, how much less in the heavenly temple of his presence?