In this context it means that Trump's attitudes are likely to trickle down, or spread down to the broader population. Ordinary people will then feel encouraged and empowered to vilify people based on their religious beliefs and ethnicity.
The expression "percolate down" has to do with coffee, which is often prepared in a percolator. Boiling water drips onto the coffee grounds, percolates down through them, taking up the coffee molecules on the way, and then drips into the jug, which gradually fills up with coffee.