Filtering is a key step after acid-soaks, I say ... The main theory to remember is that if it's "dissolved", ie 'soluble', and NOT- a precipitate then it will just pass through the filter.
Dissolved things are 'invisible'and pass through ... all the stuff you see will get stuck in the filter.
Decanting acid-MHRB-extract a few times after chilling in the fridge does a good job. But filtering get's every last drop clear - down to the pore size you have, and you can repeat many times to be a perfectionist.
You have to do it to know what will work, but don't be in a rush - let it drip through taking overnight even.
Rue seed is oily and plugs up 8 micro pores right away, and gravity takes 8 hours to push 200 ml of 3.5g rue seed extract through a filter cone. Compare this to how 200 ml of lemony MHRB extract(ground to dust) is filtered through 8 microns in 20 minutes.
Just try things to prove what you like - muck around with coffee filters - some types may work, but double them up or get 'good' ones. Or use 400-thread-count pillow cases, and put cotton-bolls in the funnel.