What contributed to this amendment getting on the party platform in 1996 but being removed in 2000?
In 1996, Pat Buchanan and Pete Wilson pushed for certain things to be in the platform while Dole stayed out of the platform-writing process. In 2000, Bush pushed for the removal of xenophobic language from the platform.
Its a balancing act Republican Presidents have been dealing with since Lincoln. Lincoln was against the nativist undercurrent that the GOP inherited from the Whigs, which was subsequently strengthen one large components of the American Party in the North, shifted over to the Republicans (including much of their office holders in Massachusetts for example.
The only times Republican Presidents have gone with the undercurrent, was in the 1920s, 1950s and in the 2010s. To some extent the 1880s as well, though this was the era when mouthing off about immigration could produce an 1884, or worse and 1874.