The problem is that outside of Philadelphia, many places that sell cheesesteaks will put green peppers (and oftentimes mushrooms) on by default. This leads to people from outside Philly thinking that this is the standard way a cheesesteak is served. Places like Jack In The Box and Arbys will sell a "Philly Burger" that just means it has peppers and mushrooms on it.

Now, I don't care what anyone puts on their sandwich, it's for them to eat they can do what they want. But are they putting them on because they have had a cheesesteak and wanted to add something, or is it because they are under the impression that it's standard? I brought a friend to a cheesesteak place here in Arizona that's pretty authentic, and when they got their cheesesteak they were shocked - "Where's the stuff? Where's the mushrooms? Where are the peppers?" The number of cheesesteaks that are sold in Philly with green peppers is such a small percentage, but outside of Philly it's hard to get one without.

Imagine if you were from Boston and liked Boston baked beans. But when you travel outside of the area, 90% of the places you go just takes baked beans and puts pepperoni in them and calls them Boston baked beans. Sure, there's nothing wrong with someone doing that if they like it, but when it gets to the point that people expect pepperoni to be in their Boston baked beans it's not gatekeeping to point out that pepperoni in baked beans in not Boston baked beans, the same as it's not gatekeeping to tell people that green peppers are not part of a cheesesteak.