No. A filter won't do. Calcium and Magnesium are in solution, so you can't filter them out using a taditional filter.
I think a reason people go with the potassium is because they are concerned (justifyably in a small number of people) about sodium sensitive high blood pressure. Despite the hype and hysteria, salt, or sodium, isn't bad for most people. The sodium you get from the sodium bicarbonate is very, very, small, and not likely to be a problem unless you have extreme sensitivity, and then, well, then its probably the least of your problems.
I don't dump the discharge into the septic, even though I understand it does no hard. Mine goes out the sump pump pipe into a field 100 feet from my house. The weeds, etc., seem no worse for it.