Nope.
We use our embouchure muscles for all kinds of things: facial expressions, speech, eating, kissing. Do any of those things “ruin” your embouchure? Of course not. The embouchure is made up of very flexible, agile muscles that are very capable of carrying out multiple tasks.
When people (almost always non-doublers) express concern about embouchure ruin, most of the time what they seem to be talking about is tension, or sensitivity loss, or buildup of callused tissue, or maybe strengthening the “wrong” muscles. If playing any woodwind instrument is giving you these kinds of problems, you are playing it wrong. Your embouchure for any and every woodwind instrument should be relaxed, balanced, and pain-free. Get some lessons with a qualified teacher, quickly.
Woodwind doubling presents real challenges. No need to invent fictional ones!
Great post! I think there’s probably a lot of flutists out there who have tried saxophone briefly and noticed that their flute tone would diminish right after playing saxophone so they dropped the saxophone and are left with the impression that the instruments are not compatible. Coming from a flute background originally, I have discovered this could not be more false. Initially I had similar issues, but as I developed better saxophone technique the effect lessened substantially. At this point there is very little impact on my flute tone, even if I’m playing flute immediately after the saxophone. And of course given some time between instruments there is absolutely no negative effect. I actually believe there are some great benefits to doubling. I often liken it to athletes cross training. It works the same concepts in different ways and prevents overuse of muscles. My lungs are getting the same workout but my arms, hands, and facial muscles move differently for each instrument which prevents fatigue from overuse.