The England player, who Rodgers managed at Anfield from 2012 to 2015, has been widely criticised for moving to a country where homosexuality is illegal.
"They [players] have to do what's best for them," Rodgers told Talksport.
"There are so many morality officers nowadays that are judging people."
Henderson, who was Liverpool's captain, was criticised more than most big-name players who have moved to the Saudi Pro League this year because he had been seen as a long-time supporter of the LGBTQ+ community.
In an interview with the Athletic this week, Henderson said the criticism "really hurt".
"When I hear stuff like, 'You've turned your back on us', that hurts me. I do care," the 33-year-old said.
"It's hard for me to know and understand everything because it is part of the [Islam] religion.
"So if I wear the rainbow armband, if that disrespects their religion, then that's not right either. Everybody should be respectful of religion and culture."
Rodgers added: "I know Jordan extremely well and I know the love he had and will always have for Liverpool.
"He was at the stage of his career where he probably wasn't going to be the first name on the team sheet any more.
"He's won absolutely everything. He probably fancied a different challenge and out of respect, it probably didn't feel right for him being at another Premier League club.
"So to go abroad and take on a new challenge clearly suited him."
Winger Jota left Rodgers' Celtic this summer for another Saudi club in Al-Ittihad. Many top players from Europe's major leagues have gone there this summer, including Real Madrid's Karim Benzema and Manchester City's Riyad Mahrez.
Rodgers said: "It's definitely something that makes players wobble because of the money that's talked about and what it can do for players and the legacy it can create for their families for years down the line.
"What makes [Saudi Arabia] dangerous is not only the money, they have a plan. The plan is attracting top players and looking to get top managers out there."
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