A mutual life insurance company is owned by its policyholders. A stock company is owned by shareholders. Demutualization is when a mutual company converts to a stock company, and for a whole life policyholder it matters because the dividends you receive actually come from being a part owner. The mutual versus stock comparison explains how those two answer to different people.
So what would warn you? Look at the dividend rate, and compare it to the guaranteed rate in your contract. If a company has trouble meeting and beating its guaranteed values, that's a big red flag. A company that keeps cutting its dividend rate and runs very close to the guarantee, or below it in some years, may eventually look for a way out of the mutual structure. Becoming a stock company is one way around the pressure of paying dividends.
There's a wrinkle with the new guarantees. A lot of older policies carry a 4% guaranteed rate, and newer ones guarantee less. Does a lower guarantee hide a weak performer? I don't think so. If the guarantee is 2% and a company pays 3%, it's easy to see where it stands. At a 4% guarantee it's much harder, because a dividend rate that just clears 4% looks the same from outside as one that falls to 3%, 2% or 1% and gets topped up to 4%. You only know the company is paying at least the guarantee. A lower guarantee makes weak performers easier to spot, not harder.
None of this means a mutual company that runs into trouble is about to fail, and demutualization doesn't cancel your contract. Your guarantees stay in the contract. What changes is who gets future profits.
The Q&A it came from, which also covered buying life insurance after a heart event, is in a short video on warning signs before a whole life company demutualizes.
To check your own carrier, pull the last ten years of announced dividend rates and set them against the guaranteed rate in your contract. A history that sits comfortably above the guarantee and moves slowly is a better sign than one that dips toward it. For the longer history, see why dividend rates are climbing after a decade of drift.