The rule of thumb on chilling pears in the refrigerator is its usually better if you can than not for storage purposes only. “Refrigerate pears at a temperature of 30 to 32°F and a relative humidity of 90 percent until you are ready to ripen them”. That’s not really very reasonable to think you could chill all pears. Warren is very good without being chilled just like seckle or Bartlett. California is Max Red Bartlett x Comice so It’s the same class of pear California Pear | DWN Variety Finder . Since you know refrigeration slows down ripening but doesn’t stop it that gives you more time to consume the crop. Back to your question “Stone cells have very thick cell membranes” so if your bartlett ripens to perfection on the tree it has more stone cells because it was on the tree longer. It can ripen all the way on the tree. If you use the tilt test and remove the pears at that stage you avoid that gritiness. Some pears will not ripen but rather rot on the tree instead. Bartlett is not that way. Everything I said so far is fact but now let’s get to the preference part. You have 2 types of pear growers those that believe in refrigeration and those that don’t. This article explains those that do PLENTIFUL PEARS:A GUIDE TO BUYING AND EATING THEM - The New York Times and Picking and Storing Apples and Pears
This explains those that don’t ripen pears in the refrigerator Ripening and Handling -
Back to my own practical experience it’s my opinion that if you plan to consume these pears immediately or can them they do not have to be chilled. Once the pear is off the tree no further stone cells develop. If you do refrigerate high quality pears a couple of days it can make a difference in texture. Here is why I say that, as an example last year Duchess D’ Angoulme ripened slower on the tree than normal and the flavor was better but so was the texture. Apples that ripen later have great texture and flavor. Back to the stone cells remember what they are now imagine Duchess had warm daytime temperatures and cold nights over a very long period that’s what happened last year. This shows just how many pears there were A windfall of windfalls! . What I’m getting at is California is a unique climate because it’s not overly hot it’s just right to ripen fruit. Gritiness can be a bigger problem in some climates than others. Your pears should not be gritty unless you get some storm or insect damage on the skin sometime in the development process.