There is a movement in chess endorsed by several grandmasters called “MoveForEquality”, which revolves around the idea that the black pieces should start first instead of the white pieces. The movement made me feel that white moving first is morally wrong and is somehow discriminatory on race. Is it racist that white moves first? If not, then why does the movement “MoveForEquality” exist?
No, it's not racist; it's just a convention. Or like the famous chess saying goes: "White begins, Black wins". There are other board games like Go where Black begins, or games where it depends on which variation you play.
The main problem with changing who moves first (or alternating it) is that many diagrams which have been printed (especially in opening books) would be invalidated, or at least require extra brain processing (mirroring) to make them work.
Personally, I'd rather have chess players focus on giving people from underdeveloped countries more chances to participate at the international level than something (trivial IMHO) like this. But it's a (mostly) free world and everybody may devote their energy as they deem fit, as long as it doesn't harm others.
Is it racist that white moves first?
No. According to MoveForEquality.com:
The rule was originally developed to make annotation easier, and has never been considered in the context of prejudice.
The goal of this movement was never to permanently change the rules of chess. The reversal of the rule for who goes first was simply a way "to inspire a worldwide discussion about equality" on the International Day for the Elimination of Racial Discrimination, which was March 21.