The former Liverpool captain has followed other global stars including Cristiano Ronaldo and Karim Benzema to the oil-rich Gulf state.
The influx has taken place despite frequent criticism that Saudi Arabia's lavish spending amounts to "sportswashing" - an attempt to shift the focus from its record on human rights.
Homosexuality is outlawed in Saudi Arabia, prompting questions over how Henderson can play for a club in the Middle East nation while upholding his support for gay rights.
Pride in Football, a network of LGBT+ fan groups, said the England midfielder had "lost the respect of so many people who valued and trusted" him.
But Southgate said the England midfielder's beliefs had not changed.
"I don't think he's changing his view on what he believes in," he told Talksport radio. "So now we're in a really complex world where, what are we saying, nobody should go to (Saudi-funded) Newcastle?
"Should nobody work for companies that the Saudis own in London or should nobody buy oil from the Saudis?
"I think it's very complicated. I completely understand the argument of, you know, you've supported the LGBTQ community and I can understand why they would have a really strong view on it.
"I think it's so difficult to say, you know, 'Is Henderson saying he doesn't support that community anymore?' Well no, he isn't, but of course people are going to say his actions are the reverse of that."
Southgate said the midfielder had previously expressed concerns to him over whether the move could affect his continued involvement with England.
"I spoke to him in the summer," said Southgate. "The question he wanted to know was, 'If I move here, are you going to automatically rule me out?'.
"We would be stupid to do that. Why would we rule anyone out based on where they are playing? We have got to see how they are playing."
But Southgate admitted: "Henderson won't be playing in the Premier League. He won't play in the Champions League, which is the easiest assessment for the level he is playing at."
