If you're a stepfather then your stepchild doesn't see you for who you are. Instead, your stepchild superimposes over you, this cultural narrative that exists on TV, radio, memes, and advertisements. Your ability to define yourself to your stepkids is overpowered by the societal construct that had already pre-defined you in their eyes. They don't see you, they see the ideal that was crafted by profit-hungry writers and content-creators.

Unfortunately, the societal narrative created around stepfathers is just disgusting. If you watch ads, TV shows, movies, etc, then you'll learn that stepfathers are abusive, or are assholes, or have drinking problems, or sexually harass their children, or are so deeply flawed and have to prove themselves to earn their families love, or all of these things at once. The amount of space that the real you takes up in people's minds is much much smaller than the amount of space consumed by the "abusive step dad" trope.

Also, stepchildren will have a trope about their biological father. Nobody ever presents noncustodial fathers as people with agency to choose when they're ready to become parents. Nobody ever presents noncustodial fathers as victims of biased custody courts that deny them equal access to their own children. No! Noncustodial fathers are always shown as deadbeats and are worthy of scorn. Your stepchild will often resent their biological fathers in ways that mimic the way noncustodial fathers are present fathers on TV. And this hatred of their biological father will impact their feelings towards you, their stepfather.

Since your wife will not experience this discrimination it will be invisible to her. She's just in a different intersection from you, how can she understand your struggle if she doesn't face it? So she won't know that she should use her privilege to stand up for you, and even if she does then she won't know how.

It's really disheartening. I wish somebody had told me that being a stepfather just meant living with somebody who hates you for reasons that are totally outside of your control.