Are There Any Risks to Your Stylus From Using Magic Eraser

Ditto for catcher10.  I would not recommend "scrubbing", or any horizontal movement of the stylus, while it is in contact with ME.  Up and down only.  I happen to own a lab grade microscope, and I inspected a few styli before and after ME, using only up and down contact.  It works. Someone recently informed me privately that Peter Ledermann frowns upon ME because he has seen some styli that have acquired shmutz from the ME, thereby causing aberrant wear and audio distortions.  I would be interested to know how ME was used in those cases, but I do take PL seriously.

ME is sooooo freaking cheap that soon as I see it getting any slight discoloration I flip to another side or simply cut a new pc.

Shmutz might happen if you use the same spot over and over.

And you don't think you get schmutz on the front sides of the stylus? 
Wiping the stylus from back to front will remove all the lint and if your records and playback method are pristine that is all you need to do if you see lint on the stylus. However if you records were exposed over time to cigarette or other smoke, cooking fumes or pollution like in LA, the stylus will collect a layer of tar. If you look under a microscope what you see s a ball of schmutz with two opposing shiny slits at the tip which are the contact patches. A brush might remove a little of this but far from all.
Last stylus cleaner is the same chlorofluorocarbon (Freon) they use as a record preservative (which it is not). It is a great solvent and will clean the stylus (and records) nicely. I would use an artist's brush. Nice and soft. If you want to save a lot of money just get a can of fluorinated brake cleaning fluid, basically the same stuff. Regardless of what someone is about to say it will not hurt anything. You could easily use Last Stylus cleaner to clean your brakes. Same stuff. 
As always the best way to keep our records and stylus clean is don't let them get dirty in the first place. Now, no matter how good you are at this occasionally some lint is going to get caught on your stylus which you can see and wipe off. By the time you can see the schmutz it is late in the game and you are spreading it to your records where it is coming from anyway and you have a mess. Do not let people smoke, cook or live in LA near your records. If you are going to buy used records you need an ultrasonic record cleaner with a little more than distilled water in it say just a tsp of Triton X-100 and a tsp of alkyl dimethyl benzyl ammonium chloride 1:750 (benzalkonium cloride) to kill the fungus.

Most of us M.E. users also use it in conjunction with brushes and/or gel cleaners - all 3 in my case (I have both the Onzow and DS Audio gels). There is no "schmutz" to be accumulated unless you’re doing this totally wrong. Long bristle brushes should be used at multiple angles/approaches, and up & around the cantilever too. Use your head, guys. And if you rotate-scrub correctly with the M.E. it never exceeds or even approaches the lateral/snag forces your stylus already sees by say, being cued into a lead-in groove or running into the end of a lead-out (the M.E. is far more compliant than a vinyl groove too, so it absorbs a lot of any lateral forces). The fear mongering over this stuff is hilarious to see.

Styli can fall out on their own due to normal use. It’s part of the wear and tear inherent to vinyl playback, combined with sometimes less than decent designs & implementations (or a bad sample). I posit that if an M.E. or gel cleaner eats a stylus from a simple dip, then it wasn’t the M.E. or gel’s fault. It was caused by a defective cartridge or prior damage, finally manifesting in failure. That stylus was likely a GONER anyways on the next LP. So anecdotal tales of M.E. / Onzow eating a stylus are only good for an "lol" reaction for me. 

Think it's just you and me Mulveling.
Likewise I still use Onzow and brushes and Last fluid.
I'm more likely to damage a stylus or cantilever when swapping carts than using ME.