"Generations": It's fused to his "neural net"....
"First Contact": It can be turned on or off at will...
"Insurrection": It can be removed. (He didn't take it to go "observe" people, people with emotions. One would think it would be when he needed it the most but whatever...)
"Nemesis": Emotion chip? What's that? (Data's back to his initial self....)
I bloody hated those inconsistencies at the time, regarding the TNG cast reunion parties masquerading as big screen action-flick movies. Continuity can be a bear, it's easier to gloss over or try to create explanations if what's made really works (e.g. how Khan knows Chekov, etc), but the advent of home video into the 1990s onward, combined with the last couple of decades with intertwining season-long (or more) story arcs, combined with word processing and full-featured script writing software such as "Final Draft", are some reasons why continuity is far more a deal now than back then.
At least generally speaking.
But GEN was still recent enough, and featuring a prominent enough scene (and entire walloping subplot!!) for a prominent character, there's no way for STFC (and onward) to be so cavalierly and grossly inconsistent. As with other things with the TNG reunion parties, the excuses got even more feeble and adding to the consensus at the time of "Trek Burnout".
If STFC onward were actually more than slick-looking eye candy, we'd all sit there and think of reasons such as "Geordi whipped out his big de-soldering iron to remove the chip and later added a socket so Data could put it in and take it out at will" or "Data added a new subroutine to compensate every time the chip was accessed", but Data is still a machine and a computer thinking independently of its programming is something best left to idle fantasy because Data would end up becoming Lore 2.0 soon enough. Actually, that almost sounds cool... if not a little cliche... but that would have been more watchable than a bunged up clone, complete with old photo of young-Picard being bald where TNG TV showed young-Picard having more hair than the
chia pet version of him... not sure what's more insulting, thinking the audience is so thick they don't remember the TV show so for "character relating" they put in a bald photo as lame tokenism, or chia pets being an actual product sitting on the shelf next to that pet rock that has yet to grow and take over the city with...
Also, TNG did jump into the movies a bit too quickly and there was no real development for anyone. Worf came back, always for contrived reasons, with each movie being more and more lax. Even STFC's and they missed out with bringing in the proper DS9 crew, but then we'd have a nerdy Sisko vs Picard grudge match and that's not as exciting as the Borg's magical new powers with kinky nanotubules...