I was just talking about this here the other day, but the Washington Free Beacon goes into more detail.
According to documents obtained initially by families who requested public records, Walmart has been facilitating public school teacher training from the Racial Equity Institute, which also does Walmart's own internal DEI training. Walmart, or foundations funded by Walmart or the Walton family, has also facilitated similar training for other organizations in Arkansas, like arts non-profits, business leader organizations, the University of Arkansas, etc.
One aspect of Walmart's influence that the article discusses is the impact of being the biggest philanthropic organization in an area. Everyone who wants to curry favor in the hopes of getting grants will take Walmart's positions into account.
Walmart also donates to both major political parties, giving about equally to Democrats and Republicans.
However, a couple of things I didn't know is that, despite Walmart's opposition, Arkansas legislators in 2021 banned transgender surgery for minors over Gov. Hutchinson's veto, and newly-elected Gov. Sanders signed an executive order banning critical race theory in Arkansas schools. So, their influence has limits.