Combine sugar and gluten-free beer in a tall pot over high heat. Mixture will double in volume as it cooks and bubbles up, so the pot needs to be large. Using a wooden spoon or silicone spatula, stir until sugar melts (sugar won’t sound crunchy as you stir), about 1 minute.
Once sugar melts, let mixture boil without stirring until caramel reaches a deep amber color, about 5 minutes. If using a candy thermometer, cook only until mixture reaches 180°F. (If it turns brown or smells burned, it is overcooked.)
Remove from heat and whisk in dairy-free buttery sticks until completely melted and combined. If using coconut milk, shake the can of coconut milk and measure out ½ cup. Whisk coconut milk or heavy cream into mixture. When smooth, stir in salt.
Transfer sauce to a glass container and refrigerate until cooled. If refrigerated overnight, cover when cooled. Bring to room temperature before serving.