1. I thought it was going to be Beast, but it's not.
Beast is a founding member of the X-Men in X-Men #1 (Sep 1963). He remains a member of the team until they stop printing new issues as of issue #66 in March 1970: https://marvel.fandom.com/wiki/X-Men_Vol_1_66
It's mentioned in passing in Giant-Size X-Men #1 (May 1975) that Beast had at some point left the X-Men.
Beast joins the Avengers in Avengers #137 (July 1975)
He leaves the Avengers in Avengers #211 (Sept 1981)
Beast joins the Defenders in Defenders #104 (February 1982)
He stays with that team through the remainder of its run, before they disband in Defenders #152 (Feb 1986) (a Secret Wars II tie-in).
From there Beast immediately joins the re-formed X-Factor in X-Factor #1 (Feb 1986) along with his long-time Defenders (and previously X-Men) teammates Angel and Iceman.
Beast leaves X-Factor (the team reforms entirely, kicking off one of the best runs on any Marvel book of all time as Peter David takes the helm with a brand-new, entirely dysfunctional group) in in X-Factor #70 (Sep 1991) and re-joins the X-Men in X-Men #1 (Oct 1991)
It turns out that all Hank's team memberships throughout the 70's and 80's were entirely sequential and never overlapped. I'm actually quite surprised.
2. It's also not the time Reed and Sue joined the Avengers (Feb 1989)
In Avengers #300 (Feb 1989), during the Inferno crossover event, Sue and Reed Richards apparently joined the Avengers for a while: https://marvel.fandom.com/wiki/Avengers_Vol_1_300
However, they were not in the Fantastic Four at that time, cf. https://marvel.fandom.com/wiki/Fantastic_Four_Vol_1_323
So this is a near miss - even though the cover art does show them in the iconic FF unis.
3. It's also not the time the Thing was briefly in West Coast Avengers (June 1986)
Ben was an official member of West Coast Avengers in West Coast Avengers (vol 2) #9 (June 1986). https://marvel.fandom.com/wiki/West_Coast_Avengers_Vol_2_9
But this occurred during a period of his absence from the FF (replaced by She-Hulk): cf. https://marvel.fandom.com/wiki/Fantastic_Four_Vol_1_291
4. At one point I thought it would be Secret Defenders #1 (March 1993)
Marvel relaunched the Defenders as Secret Defenders in March 1993 where Dr. Strange recruits various teams of heroes to face individual threats. Wolverine is featured in the first three issues. Assuming one counts this as superhero team membership, this is another Wolvie cross-team situation.
5. It can't be any later than Fantastic Four #347 (December 1990)
...And then I remembered this one. One of the few times my young self bothered to purchase a few issues of FF.
A Skrull KO's the entire FF and recruits a "new Fantastic Four" to serve in their stead, leading to a three-issue arc where Hulk, Spider-Man, Ghost Rider and Wolverine comprise the team.
Wolverine is still in the X-Men as of this period (cf. Uncanny #271 https://marvel.fandom.com/wiki/Uncanny_X-Men_Vol_1_271).
So it may or may not be the first instance, but at worst we have an endpoint from which to work backwards. On another personal note, this arc features some really incredible pencils from Art Adams.
I couldn't find any instances earlier than this!
6. Important Note re Crystal
If you you consider the Inhumans a "Superhero Team" (I do not), then the answer is Crystal, who officially joins the Fantastic Four in FF #81 (Dec 1968), presumably coincident with her 'membership' in the Inhumans. https://marvel.fandom.com/wiki/Fantastic_Four_Vol_1_81