Just read the following at Bill James' Hey Bill page:

Bill, in a recent NBA playoff game, Cleveland Cavalier Rodney Hood refused to enter a game in garbage time. Have you heard of this happening in MLB?
Asked by: Steve9753

Answered: 5/24/2018
I have, yes. We had a player with the Red Sox who refused to take a garbage-time at bat in 2014. He was a pretty good player and I liked him, but you know, you can't have that. We released him, and his career ended a couple of weeks later.

Also, about 1979 or 1980 there was an opposing player in a Kansas City Royals game who refused to play in a situation like that. It got into the newspapers, I think. I remember it because we were talking about this player while working on an arbitration case, and Joe Sambito got very offended that I would say that a major league player had done such a thing. But he had. Can't remember now who the player was.

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I looked up the 2014 Red Sox page at b-r.com and the best candidates ("pretty good player" who last played in 2014) would appear to be Ryan Roberts and Mike Carp. Both of their MLB careers ended in 2014, Roberts' with Boston and Carp's with Texas 17 games after being claimed off waivers from Boston.

I can sort of see a pitcher being ticked off about being relegated to mop up duty, but why would a hitter object to an at bat, even a "garbage time" at bat?

I'm also curious about the second player Bill James is referencing from 1979-80 but I figure it's a long shot that anyone here would know that...

I remember that Ken Holtzman refused to go into a game for the Yankees when Billy Martin was the manager...Martin hadn’t used Holtzman in a month and when Martin told Holtzman to warm-up, and subsequently, enter the game, Holtzman always replied that he wasn’t ready yet...They hated each other...

Thanks for that info. Here's an NYT article from 1977 that's possibly referencing the game Holtzman didn't want to pitch in (exhibition game against the Yankees' farm team).

I seem to recall Cecil Cooper declining to play near the end of his last season with the Brewers. I don't think it was during a game just in general when offered the chance to play near the end of the season he declined.

I think sparky lyle refused to come into the game where Reggie bunted on his own

Still curious about this but couldn't find anything. But it reminded me of the time the Patriots were playing the Bills in `98. The Bills defense refused to come out on the field to defend a meaningless extra point with the clock at 0:00, so Pete Carroll had his team go for two.

https://imgur.com/a/nAMgX#mXq0b43

Gary Sheffield took the field at least.........