The even shorter tl;dr:
Registering to vote will become much more difficult for millions of people. Joe Blo should care because he might be affected, and even if not, many friends and neighbors will be. Trump cares because he believes that difficulty will be concentrated on women, minorities, and the socially disadvantaged in a way that is beneficial to him personally.
https://www.vote.org/save-act/
This is a good, easy-to-understand summary of the act and its consequences.
Other links for the interested:
https://www.congress.gov/bill/119th-congress/house-bill/22
https://en.wikipedia.org/wiki/Safeguard_American_Voter_Eligibility_Act
The even shorter tl;dr:
Registering to vote will become much more difficult for millions of people. Joe Blo should care because he might be affected, and even if not, many friends and neighbors will be. Trump cares because he believes that difficulty will be concentrated on women, minorities, and the socially disadvantaged in a way that is beneficial to him personally.