When did the word "guys" become popular as a gender-neutral word?

Solution 1:

It has not always been the case. The term "guy" first referred to "an effigy of Guy Fawkes traditionally burnt on the evening of November the Fifth, usually with a display of fireworks" according to the OED; this sense is first attested in 1806.

The word first began to refer to a man or group of men in 1876, also according to the OED's examples.

Unfortunately, the OED is not clear on when it began to be gender neutral. However, I did find some other sources that try to answer that question.

“Denotatively, this is an established use of ‘guys’ to mean ‘people’ — that use goes back a while, probably to the mid-1900s,” said Kory Stamper, a lexicographer and editor at Merriam-Webster.
_{An unnecessarily long and surprisingly fascinating history of ‘guys’}

Macquarie Dictionary senior editor Victoria Morgan said in Australia, teenagers started using "guys" as a gender neutral term in the '80s and it has been since been used to refer to groups of people of both gender. She added the word "guys" was not a term that carried an inherently sexist connotation and came into usage without any power struggle between the genders.
_{Hey guys: Oxford, Macquarie dictionary experts say using 'guys' is not sexist}

It is important to note that "gender neutral guys" is used in other dialects of English, notably mine (as this graph shows, pretty much everywhere in America uses it except for the south).

Solution 2:

The Southern American translation of "Hey, you guys!" is "Hey, y'all!", which suggests that the informal second person plural guys addressing a mixed gender group is 1) the same inclusive/generic masculine that's been around for centuries, but 2) is perceived by those using the form to be gender neutral, and 3) the source of other plural uses in the third person that may seem gender neutral or not depending on circumstance and audience.

Wiktionary has the following usage note:

In plural, guys is not completely gender-neutral but it may refer to people of either sex in some circumstances and forms; the greeting “Hey guys” can generally refer to people of either gender. This usage is not always seen as accurate or correct. Referring to a group as “guys” usually means a group of men or a mixed-gender group, since describing a group of women as guys, as in “The Pussycat Dolls are a bunch of guys”, suggests that they are male, and is generally viewed as incorrect or inaccurate in that usage. In contrast, the all-male band Green Day could accurately be described as “a bunch of guys” in slang. The usage of the plural guys in the phrase “some guys chased them away” would generally be assumed to mean men rather than women. When used of animals, guy usually refers to either a male or one whose gender is not known; it is rarely if ever used of an animal that is known to be female. In some varieties of US and Canadian English, you guys revives the distinction between a singular and plural you, much like y'all in other varieties; in this sense, guys is gender-neutral.

You can also read there how the etymology really goes back to Guy Fawkes and that in earlier centuries, a woman dressed like a guy most likely wasn't in a flannel shirt, jeans, and workboots.