I just recovered two big (6") chunks of a bouyant, white chalky pipe-blockage from my tank. No, it is not slippery. It feels like one might expect wet chalk to feel, or joint compound that has about 90% of the stickiness removed. There is a bit of black nastiness on the outside, but the inside is surprisingly white for something from a sewer pipe. Right now I have samples soaking in bleach and vinegar.
In general terms, there are only three things you could pour down the drain besides water to fix problems: A base (high pH), an acid (low pH), or an organic solvent.
One would be silly to pour an organic solvent (i.e. gasoline, paint thinner, acetone, or dry cleaning fluid). If you didn't dissolve plastic pipe, set the house ablaze, or seriously pollute the environment, you still probably wouldn't dissolve enough to make a difference.
A base is great stuff. It turns grease into soap. It denatures protein (including hair). You probably have baking soda (weak) or bleach (not quite as weak) in the house. If you need more, buy lye or drain cleaner (lye in a fancy bottle).
Acid will dissolve calcium deposits. I have calcium deposits in my shower nozzles and in my toilets, but I'm not convinced it filled my sewer line. Here is one bit of chemistry you should know, though: calcium salts are less soluble in hot water, so dumping hot vinegar in your drains is counterproductive.
In the acid lineup, 5% vinegar is the starter. Citric acid is good for freshening your dishwasher, oxalic acid takes cat-pee stains out of a wood floor, and manly men use muriatic (hydrochloric) acid to clean up bad tiling jobs. They also use gloves and glasses and ventilation.
Too much of either acid or base will kill every microbe in your septic system or sewer. When the microbes wake up from the dead, it may smell bad. Use of chemicals may cause junk to flow out into your drain field. Any one of these events can be smelly or expensive.
When you read helpful hints on the internet, any solution that tells you to mix baking soda and vinegar is wasting your time. It bubbles -- remember the volcano you made in fifth grade? After the two mix and make CO2, you have no more acid or base. You might as well use plain water.
My sample soaking in bleach has lost some integrity. No ferocious reaction or bubbles, but the sample is breaking up. The sample soaking in vinegar shows no change. It may be dissolving, but it's not visible. My lab is just two Pyrex dishes on the counter. Your mileage may vary.
A little more chemistry before I finish this rant: soaps aren't what they used to be. When your grandmother loaded her washer and dishwasher in the 60's, she had the best chemistry industry could provide: tri-sodium phosphate, a really great surfactant (detergent). It was removed from clothes washing detergent twenty years ago and from dishwashing detergent ten years ago. You thought your dishwasher wasn't working well anymore? Nope. The new soap is no good. It has some cool enzymes to breach down food protein, but wimpy detergent to take care of grease. It isn't as good a fertilizer, either, so it doesn't cause blooms in river and lakes.
If you don't feel comfortable with the concepts here, swallow hard and call a professional. You may not like the answer, but at least it's not one made up be someone on the internet. ;^)