As a new step parent, I struggle with matching my parenting style to my spouse's. How do you do that, especially if your styles are very different?

Sitting down and talking with your spouse can help a lot, if you both want to resolve the tension this causes. It helps to talk about what you want the end goal to be in raising the children, and values and habits you want them to have. Focusing on those end goals can help bring you two together in parenting. Also, it's important to not correct or contradict each other in front of the kids, but to support each other's decisions and talk about the issues in private later if needed. This will show the kids you are united in raising them.

Compromise is the key for any relationship but this is massively magnified in the step-parent relationship. As the bio parent your spouse needs to take the lead adn for you together to work out how you can support them in that and where changes need to be made