The 'Mysterious Girl' singer and his ex-wife, model-turned-businesswoman Katie, are parents to son Junior, 11, and daughter Princess, nine.
Katie, 39, revealed on ITV's Loose Women last month that she's allowed the kids to sign up for Instagram accounts, which they use to stay in touch with school friends and manage their professional bookings.
She's said she keeps full control over everything they see and do on the site, and both Junior and Princess' Instagram bios specifically say the accounts are run by Katie.
But Pete doesn't seem as keen, writing in his latest New magazine column: "Everyone knows I don't allow them to have phones or social media at my house, but I guess it doesn't necessarily mean to say I'm right.
"I don't like kids having them because I think it opens them up to all sorts of issues, but as a parent you have to compromise with the other parent and try to work together. I can only advise and encourage them – I can't do any more."
Peter, 43, who is also dad to Amelia, two, and has another baby on the way with wife Emily, said something similar in an interview with OK magazine, commenting: "I'm not a fan of social media for kids. If they are going to do it, I'd like it to be a private account.
"I don't allow them to have phones when they're with me but, like I said, I have to compromise. Every parent is different – it doesn't mean one is right and one is wrong. I'm sure my way isn't always right."
On Loose Women recently, Katie - who has three other children, Harvey, 14, Jett, three, and Bunny, two - defended her decision to open Instagram accounts for Junior and Princess, saying it's just Instagram they are allowed to use: no Facebook, Twitter or Snapchat.
She said: "My kids have been brought up in the industry through their dad and me, TV shows, everyone knows who they are. Now they're being booked themselves to do TV shows, modelling jobs and that. Social media is the future."
Katie went on to say that many of Junior and Princess' friends have their own Instagram accounts, some private and some public, so she made the decision to allow them to join the social networking account after they repeatedly told her they wanted to.
"I said, 'This is the deal: if you want to be on Instagram I have your password, you go on it when I'm next to you, you don't go off it at all.' I sign them in and sign them out. I vet everything, block everyone who is nasty. I made it clear they don't follow anybody on it. Anyone who tries to direct message them, I block it and take it off. I'm in absolute full control of it."
Watch Katie discuss her kids' Instagram accounts below: