There is a lot of debate surrounding the best type of brush to use when applying muriatic acid. Some say that a natural bristle brush is best because it won't dissolve in the acid like synthetic bristles can. Others argue that a synthetic brush is better because it's less likely to shed bristles into the acid. Ultimately, the decision comes down to personal preference and what you're comfortable with using.
If you do choose to use a natural bristle brush, make sure it's made of boar hair or another material that can withstand harsh chemicals. And be sure to rinse the brush thoroughly after each use to prevent the acid from eating away at the bristles.
Synthetic brushes are also a good option for applying muriatic acid. Nylon or polyester bristles are less likely to shed than natural bristles, and they're also resistant to damage from harsh chemicals. Just be sure to choose a brush with firm bristles so that they don't bend or break when wetted with acid.