Henderson joined Saudi Arabian club Al Ettifaq from Liverpool in the summer, a move widely criticised as being at odds with his previous public support for the LGBTQ+ community. Homosexuality is illegal in the Middle Eastern country.
The former Liverpool captain was met with hostility from the stands on his return to Wembley in Friday's 1-0 friendly win over Australia.
"People might disagree with Jordan's stance... but I don't think it's a reason to not select him and I don't actually think that's a reason to boo him," Southgate told reporters on Monday. "We'd like all the fans behind us.
"I'll always pick the players I think... give us the best chance of winning, unless there's something that I feel is not appropriate.
"If I just select on a popularity contest then our team would look very, very different."
England full back Kyle Walker (32) also stood by his teammate.
"I've known (Henderson) since the age of nine," Walker said. "I fully back Jordan, his decision and what he's had to do."
England top Group C with 13 points from five matches, three ahead of Italy who beat them on penalties in the Euro 2020 final.
"Teams learn from finals and setbacks and go on to achieve," Walker added.
Southgate's men beat Italy 2-1 in Naples in their first Euro 2024 qualifier in March and have won three of their next four matches in the qualifying campaign.
England will book a place at next year's finals in Germany with a win or draw against Italy.
"Our performances earlier in the group have put us in a strong position," Southgate added.
"We want to play well and win the game. If it's the 87th minute and we're level, we don't need to lob (send) the goalkeeper into the box."
