But you miss the point ( they're vs. their).
''Unless they're trash'' makes grammatical sense, and describes the dreams as being useless. "Unless their trash'', on the other hand, implies that the trash belongs to an entity as yet unknown; it's not Sam's trash, or sue's brother's trash, or your neighbor's trash. You simply said it's "their" trash.
And I'm showing concern. I'm showing I care. I'm interested in your thoughts and hopes and desires and interests and aspirations and loves and views on life & the universe & everything! And I just wanted to know WHOSE TRASH was the meme talking about?