The 18-year-old, who was born in Belgium, could be eligible to represent the country he currently plays in due to FIFA residency rules.
"People are always complaining that players don't have an opinion or that they say nothing worth listening to, so I don't think it's quite right to criticise someone for having an opinion," Hodgson said in a press conference.
"The subject matter is worthy of debate and, at the end of the day, it will be a policy decision taken by the FA. From my point of view, it hasn't affected Jack. I think he just shrugs it off.
"He's put behind him the unfortunate furore over his quotes and it's not affected him one bit on the field. I think England will get a lot out of him in these next two games and for a long, long time to come."
Wilshere is likely to start for England in their World Cup qualifier against Montenegro on Friday.