While I believe Linux is a more reasonable operating system than Windows, shit can happen everywhere.
So if you have truly mission critical systems you should probably have more have at least 2 significantly different systems, each of them being able to maintain some emergency operations independently. Doing this with 2 Linux distros is easier than doing it with Linux and Windows. For workstations Macs could considered, for servers BSD.
Probably many companies will accept the risk that everything goes down. (Well, they probably don't say that. They say maintaining a healthy mix is too expensive.)
In that case you need a clearly phased approach to all updates. First update some canaries used by IT. If that goes well update 10% of the production. If that goes well (well, you have to wait until affected employees have actually worked a reasonable time) you can roll out increasingly more.
No testing in a lab (whether at the vendor or you own IT) will ever find all problems. If something slips through and affects 10% of your company it's significantly different from affecting (nearly) everyone.
What makes you think windows is the only alternative? Have you never heard about Gnu Hurd?
More seriously I am not saying you should run some critical services on menuetos or riscos but the BSDs are still alive and kicking as well as illumos and its derivatives. And yes I think a bit of diversity allows some additional resilience. It may necessitate more workforce but imho it is worth the downsides.
