Why does Merchant Center say my Shopify product has mismatched availability?

Short answer

The availability your store sent to Google differs from what Google reads on the product page. Google says the two must be the same, and that too many products with incorrect availability can lead to account suspension. Look at the page as a shopper, at the page's structured data, and at how the product's inventory is set up in Shopify.

What Google compares

Google holds an availability value for every product. It also visits the product page. Google says the value in your product data and the information on the landing page must be the same, and that too many products with incorrect availability can lead to account suspension.

Google asks for a consistent availability in four places: the landing page, the page's structured data if it has any, the checkout page and your product data. For an in-stock product it expects an active buy button.

The four values

In stock: you are accepting orders and can fulfill them.
Out of stock: you are not accepting orders, or the product isn't available for purchase.
Preorder: you are accepting orders, but the product has not been released for sale.
Backorder: the product isn't available at the moment, but you are accepting orders and will ship it when it is.

Google asks for an availability date when you submit preorder or backorder.

Where to look on Shopify

Open the product page as a shopper and note what it says: a working buy button, a sold-out label or a preorder message. Compare it with the availability Merchant Center shows for the product.
If the product has variants, open the exact variant Google flagged, not only the product's default page.
Look at the inventory settings. Shopify says an item is out of stock when inventory is tracked and the level is at zero or below, and that by default customers can't buy it. With Continue selling when out of stock selected, they can. Make sure the page and the product data describe the same situation.
Run the page through Google's Rich Results Test and read the availability in the product markup. Google calls structured data for availability crucial. If the markup says in stock while the page says sold out, the theme or an app is writing the wrong value.
If you take preorders, check which value Merchant Center holds. Preorder is its own value, and Google wants a date with it.
Don't mark a product out of stock to keep it off Google. Google says not to use out of stock to pause a product. Shopify lets you change a product's availability to the Google & YouTube channel, for one product or in bulk.

If stock changes often

Google recommends scheduling product data updates to coincide with updates to your store, and using automatic item updates when that isn't possible or when prices and availability change often. With automatic item updates on, Google corrects the availability itself and reports "Automatic updates: Mismatched availability". Google says the settings are on the Automations tab, which you reach by clicking Products.

Getting it checked again

Fix the cause first. Then in Merchant Center open Products, go to the Needs attention tab and request a website check. Google says the review can take up to 12 hours, and you can't send another request during that time.

Questions

Is the product disapproved?

It can be. Google says it disapproves a product that doesn't follow the availability requirements, and that too many products with incorrect availability can lead to account suspension.

Can I set a product to out of stock to stop it showing on Google?

Google says not to. It points to its pause attribute, which pauses a product for up to 14 days. On Shopify you can make the product unavailable to the Google & YouTube channel instead.