Glass jar with starter in broke... how to rescue the starter

I wouldn't take a chance.  Regardless of how good the starter is, do you really want to risk having broken glass in the bread?  I'd say throw it all out, and start over.  Better safe than sorry.

just what you did. rinse as much as it as I could gather through the finest mesh I could find, then feed the water with equal weights flour.

Keep a small jar of backup starter in the fridge to recover from such disasters (or mold). You can use it as inoculum for a new batch of starter. Anyway, the starter with the broken glass all has to be discarded.

Here's what I would do.  Wait for the starter to mature, and the gluten to thin out.  Add water to make it into a milk and pour it thru a coffee filter or paper towel lined sieve.  

Take the milky water and add flour to feed.  finish.   Problem glass is in the paper towel because yeast and bacteria are so small they will pass thru the paper towel or paper coffee filter.  :)

What you did with the fine tea strainer is just as good. 

I think it is foolish and dangerous to try to salvage any kind of food with broken glass in it, I don't care what you strain it through. I would err on the side of caution and make a new starter if you don't have some backup inoculum. It only takes a week and you'll be as good as new.

Don't worry.  Same thing happened to me.   Just scoop a teaspoon (or more) of starter (being careful not to cut yourself) and set aside while you clean up the mess.  Now you just rebuild from this new "mother."  Add a cup or so of lukewarm water to the mother and equal amount of flour (in an appropriate container).  Let it sit in room temperature covered for at least 8 hours.  Starter should show signs of life.  Discard half and feed the rest with half cup water and cup of flour.  Cover and let sit.  Keep doing this until you have the quantity of starter you need.

I would do as MiniOven said.

I do have glas jars with screw necks but I am looking for a plastic container such as AbeNW11 has.

Mine would need to hold 100g of starter that will be fed with 100g water and 100g flour. hmmm

For now I have mine in a widemouthed Ball Jar.

glass Mason jar full of starter on the floor, I recovered by taking a bit making a liquid out of  and pouring it through a strainer lined with a paper towel.  Now, for a couple of years, I have stored my starter in the fridge in a plastic container that store bought frosting for cakes came it.  Perfect food grade plastic that has a lid,   I also build my levains in them too,

my rye starter is chilled in the 500ml plastic beaker that came with my mixer wand some umpteen years ago.  It came with a snap on lid and the sides are marked.  I like deli pint size containers too, can stack them up in one spot, oldest on the bottom and I like glass stackables as well.  

So break a glass jar ever so often, shouldn't be big deal.  Also when the little glass pieces are in a milky sourdough water mixture, the glass will sink to the bottom, just give it a chance and pour slowly off the top and throw the bottom bits to the trash.   

There is a certain security with glass that plastic chemicals are not in constant contact with the starter.  

I've been trying to cut down on plastic for food storage.  I use the small 8oz Bell jars.  No breaks so far.

If you are in the States, the type of item below goes under the brand name of Tupperware, but it has become a generic description of pretty much any softish rubbery plastic food storage tub.  I keep my stiff levain culture in one of these containers in the refrigerator, with a plastic film tucked tightly on top to keep any ambient air from hardening up the surface.  This only gets refreshed once every ~3 months, so it lives there a long time, and the container never gets washed.  

Just for some ideas for the future - I also keep a backup thumb-sized piece of stiff levain wrapped tightly in plastic film elsewhere in the fridge, some frozen levain from 9 months ago as well as dried flaked levain to revive kept in a jar in the cupboard.  All as a hedge against any issue with the current batch.  And also in the event of a nuclear disaster, I'm ready ;-) .  Over the top?  Sure.  but the price of doing it was a few minutes of my time, zero cost and provides a host of options.

Sorry about the glass issue, I would not take the risk, although other folks seem to speak from personal experience. 

I would do the coffee filter if the starter is not replaceable

 and when you get it going or replace it dry and freeze some as a backup

 the dollar store has nice drinking cups made of plastic that have a little hole for a straw tape a coffee filter or gauze pas over the hole to keep fruit flies and stray microbes out of your starter 

What's the resistance to making a new starter? You may have to do this someday if your starter goes moldy.

I store my starter in a glass jar in which preserves are sold (jam, jelly, marmalade). It has a metal lid which doesn't screw on like a mason jar. It just takes a little twist and it's sealed. It would take a lot of work to over-torque the lid. The lid is also lined with plastic. You could also use a baby-food jar but they have a pretty small capacity.

I prefer not to store my starter in polyethylene plastic, such as Tupperware.