Not quite clear about how many people on this thread are step-parents and if so how engaged people are in the step-parenting role.
But the way I see is is that you (Person A) shack up with a partner (Person B.) The two of you may have various differences in terms of politics, religion, social attitudes etc. However it's likely that you have some things in common, because if you disagreed about absolutely everything you probably wouldn't have got as far as moving in together. And you will have the ability to talk about and accommodate difference - otherwise the relationship wouldn't have got that far.
However your partner B was previously with a different person C. Will Person A necessarily have anything in common with C, other than the fact they have both known/know B pretty well. The differences in attitudes are likely to be bigger, and the opportunities to get together and get to know and understand each other's point of view are likely to be small. It probably won't help that B and C have split up, so that C is not likely to be represented to A in a particularly favourable light.
It may also be that a long working hours culture for B has meant that C has played a particular big role in terms of making decisions about the childrens' lives. So A will suddenly find she's spending quite large amounts of time being expected to care for children whose formative years were shaped by someone with a pretty different world view.
Some examples can be quite trivial, but they can trigger raw nerves. For example stepchildren can turn up for the weekend wearing clothes you would never ever in a million miles choose to purchase for any child of your own. Or with possessions that you would never in a million years consider having got yourself. What do you do?
For example my stepdaughter was quite plump at around the time she hit early puberty (about 10). She came round once then dressed in a T-shirt that stretched very tightly across her budding breasts. Across the front of this T-shirt were the words in large letters. 'All This and Brains Too!' I thought it was a really nasty and unsuitable garment. Clearly thought her mother didnt.
When he was about 8 or 9 my stepson was given, as many boys were, a couple of laser guns that were his favourite gift. He asked me to take one of the guns and play with him. Now I was brought up in a pacificist household where none of us were given guns as toys. I was quite reluctant to do as he asked, but judged he was way too young to understand any explanation about why I was reluctant I wasn't even 100% sure that I as an adult did think the laser guns were harmful. But I did know it was really hard - I had to overcome something - if I were agree to play this game. (In the end I did take one of the guns, and took great pleasure in ambushing my stepson and shooting him at point blank range.)
I think it is one of the key things about being a step-parent. You become closely connected to someone who may have been brought up in a very different way, and who will display that difference in little or big ways all the time. And all the time you have to think - what do I do now? What do I say? Something or nothing? What reaction will I get? What are the risks? Can I be authentically myself with a stepchild- on the basis that in the longterm this will mean we may get to like and understand one another? Or do I fake it and do not much more than nod and smile and make polite noises - as one might with a house guest?
One things for sure. It is utterly different to bringing up a child with your partner from birth.