I re-married when my DS was 10 years old. He's ND. I married someone who my DS had got to know as a 'friend of mummy's' over 5 years.
For context I was widowed before DS was born so it was just him & me for years. I introduced my BF carefully as I say, he was mummy's friend for many years & never stayed over unless DS was staying at his GP's house. It was DS who broached the subject of us getting married by asking my BF if he was going to marry his mummy and why not when BF said he hadn't asked me.
As it turned out the marriage was a disaster, but DS & my XH are still close & DS regards him as his 'father'. So in that aspect not a complete disaster, as at least DS has a father figure, just XH was a crap husband. But that's subject for another discussion.
XH felt that he shouldn't discipline DS & left it all to me. Even to the extent that he would leave the room or even the house & say 'over to you'. I've since talked to DS about this (DS is now aged 29) he says that he wishes that XH had been stronger & that he felt that he could divide us by messing around when I wasn't around without consequences & that looking back it would have helped if I'd been backed up by XH.
However, DS suspects that XH is also ND & has tried to discuss this with him, but he refuses to engage in this conversation.
To sum up: I say that a step parent is a parent & they should tell a child off if the child is misbehaving. Just as with natural parents, it should be agreed. From which I mean, both parents should be in agreement about what is acceptable & what to let go. Also need to agree with the punishments - when the naughty step, time out, grounding (and what 'grounding' means) is appropriate.
Always parents need to discuss & have a united front - at least in front of the children, you can discuss late if you disagree with a decision the other parent made.