In developed countries we use running water as a matter of convenience for washing negatives. It sounds like the tap water you will have on hand will manage to deposit all manner of crud in the soft emulsion of your just developed film.
You don't have to use running water, as used in cheap clean water areas. You can use a diffusion washing method, that takes more effort, but uses less water. That way you can use filtered water. You simply soak the negative in water to let the fixer diffuse out, agitating occasionally, dump, refill and soak again, and continue this process for ten cycles, equaling the time you would normally rinse them with running water.
When I have tried filtering muddy water, the sediment usually clogs the filter pretty fast. I have found that by allowing the sediment to settle for a day or so in a five gallon bucket, and pouring the clean water to another bucket, taking care to leave the crud in the bottom, and filtering from the second bucket to be much more successful.