This "old wive's tale" is well documented in the work of Colonel E.H. Harrison (NRA publications, 1950's to 1970's). The concern is not so much about clogging a gas port. The concerns are the internals of the gas cylinder and face of the operating rod. When leading builds up on these parts the forces required to cycle increase, applying excessive force to the operating rod and bolt in cycling, and harsh cleaning methods will be required to remove the leading, causing accelerated wear on critical parts.

These issues are more concerning today than 50 years ago. Back in those days surplus parts were readily available at very low cost, gunsmiths qualified to R&R the M1 gas cylinder were readily available for relatively low fees, and the rifles themselves were very common rather than the historical relics they have become. Today's owners of M1 Garands and derivative rifles have far more reason to avoid problems.

Your rifles, your decisions.