80’s football attendees - what games were these from

Coach was Mike Archer. Hodson was QB for most of that time. No Joe's as QB or RB then.

Obviously Bo because there was a Bo Knows commercial back in the day with Bo Jackson and Bo Diddley

Why would LSU ever make a red button? Are we sure it's ours

My best guess is that the buttons are not referencing a football game but rather the 1993 ALCS when Joe Carter and the Toronto Blue Jays beat Bo Jackson and the Chicago White Sox (even though the red writing makes little sense because the Blue Jays have only a tiny amount of red in their uniforms). Here is why....

FOOTBALL?
I believe I have completely ruled out football.

Bo Jackson played for the Los Angeles Raiders from 1987 to 1990, and he played for Auburn during the 1982, 1983, 1984 & 1985 seasons. (He sat out of football in 1986 and only played baseball.) Bo Jackson

The "Bo Knows" ad campaign began in Summer 1989. "Coincidentally, the spot first aired during the commercial break immediately following Jackson's lead-off home run in the 1989 Major League Baseball All-Star Game." So the buttons do not date back any further than the summer of 1989. Bo Knows

During his time in the NFL, the only game in which Bo Jackson played Joe Montana (including both regular season and playoff games) was Los Angeles at San Fran on November 13, 1988, but that game was before the "Bo Knows" commercials. Even still, the Raiders won that game 9-3, so it's not from that game. NOTE: The Raiders' only playoff game during that time was during the 1990-91 season - the divisional playoff in January 1991 in which the Raiders beat the Bengals (and Bo got hurt), so it's not from that game either.
1987 Raiders Roster & Results
1988 Raiders Roster & Results
1989 Raiders Roster & Results
1990 Raiders Roster & Results

Based on the red/white color of the buttons, it could be their division rival the Kansas City Chiefs. The Raiders lost to Kansas City only 4 times while Bo was on the team (Dec. 13, 1987; Sept. 17, 1989; Nov. 4, 1990; and Nov. 25, 1990). However, the Chiefs did not have anyone named Joe from 1987 to 1990 (except Offensive Coordinator Joe Pendry).
1987 Chiefs Roster
1988 Chiefs Roster
1989 Chiefs Roster
1990 Chiefs Roster

The only teams that beat the Raiders between 1987 and 1990 and have/had red as a major color were the Atlanta Falcons (Nov. 20, 1988) and the Buffalo Bills (Dec. 11, 1988 and Oct. 7, 1990).
See previous links to 1987-1990 Raiders Rosters.

But, the game against the Bills in 1990 is the only one that was played after the "Bo Knows" campaign started. Even still, the only people named "Joe" on either team from 1987-1990 were Joe Devlin (OT-Buffalo) and Joe Costello (DE-Atlanta).
1987 Bills Roster
1988 Bills Roster
1989 Bills Roster
1990 Bills Roster
1987 Falcons Roster
1988 Falcons Roster
1989 Falcons Roster
1990 Falcons Roster

Does anyone see any other "red" teams that beat the Raiders from 1987 to 1990?

BASEBALL?
Bo Jackson played for the Kansas City Royals (1986 to 1991), the Chicago White Sox (1991 and 1993), and the California Angels (1994). He was on IR for all of the 1992 season. He only appeared in 23 games in 1991 and 85 games in 1993. It was with the White Sox that he made his only post-season appearance. In the 1993 ALCS, Chicago lost in 6 games to the Toronto Blue Jays (which is not a "red" colored team). His final baseball season (California Angels in 1994) but that season was cut short by the 1994–95 baseball strike, and Jackson decided to retire at age 32. Bo Jackson

I cannot imagine MLB fans making a button for a single regular season game or series, so let's look at his only post-season appearance against the Toronto Blue Jays in 1993. At that time, the star and highest paid player on the Blue Jays was Joe Carter (the only "Joe" on the team). However, his stats from the 1993 ALCS are not great at all. He only went 7 for 27 with 0 HR.
1993 ALCS
Game 1
Game 2
Game 3
Game 4
Game 5
Game 6

So, even though the Blue Jays have only a tiny amount of red in the uniforms, and even though Joe Carter's stats were not that great, my best guess is that that the buttons were made after Joe Carter and the Blue Jays beat the White Sox in the 1993 ALCS. I simply cannot find any other team/game which they would have been made for.

Def not LSU related.

Not from LSU. The printing would never be red. I've never seen anything regarding LSU in any sport that had printing in red, and I've been going to LSU games since the late 50's.

The "we came" button is a riff on a line from "Ghostbusters" (1984).

There were tons of buttons and t-shirts made around the country with similar language, so your button may have nothing to do with LSU or even sports. Might have been picked up at a frat party.

A few million shirts and buttons with "Joe knows Football" have been sold to Penn State (Joe Paterno) people over the years. Did the wife have a Penn State connection?