No relationship with kids either bio or blended is at its healthiest if the kids are THE most important thing. Anyone's dp should end up being as important albeit in a very different way. It's like putting on your own oxygen mask first - tend to the relationship & the kids will benefit.
Indeed, however, the problem here is that for some parents, having the freedom to parent your own kids as you see fit can take precedence over the rest.
When I met my OH, I made it clear from the start that I would not in any way change my outlook in the way I raised/disciplined my kids. I have strong principles on education, and had so far invested a lot in applying them. I was not prepared to share my life with someone telling me I had to undo it all just because they didn't agree with it. It was therefore essential that they agreed with it before we considered a future together.
Of course there will always be some elements that require some compromises but that's different to expecting a more lenient parent to become stricter or the other way around.
If my OH had started to say to me a year or so after being together that he wasn't happy with the way I was disciplining my kids, having said nothing before, and expected me to make some significant changes, it would have most likely be the end of the relationship because I wouldn't have been prepared to change what was fundamental to me just to make them happy.
Some parents just go along with the role and are happy to embrace any advice on discipline, in which case, it can work very well for their partner to guide them as long as it is done in a way that doesn't build resentment with the kids.
The problem is when the parent is happy with the way their discipline their kids already, or go along with changes but this leads to only negativity in their relationship with the children potentially leading to the children not wanting to visit any longer.
There are so many similar threads here and it really sadden me that this matter seems to be one always forgotten to be discussed before moving in together and I don't understand why, unless it is insecurity that doing so might mean not moving in together and a belief that changes can be demanded later.