If you use an older edition of Shadowrun, you’re running an older edition of Shadowrun, like how people say they run PF2e. Or you saying you’d run Shadowrun Anarchy. But you wouldn’t say you’re running Shadowrun at a LFG forum and expect nobody to ask or care what edition.
House rules are house rules. They’re expected, but usually minor in the scope of the system.
Both are a far cry from “replacing the mechanics entirely”. There’s only so much you can replace or scrap before you cross a line of it not being the same system anymore, and “replacing the mechanics entirely” definitely crosses that line. It’s like when you see someone say “Yeah I’m running D&D5e but I replaced the combat rules and added Draw Steel’s negotiation system and reworked all the proficiencies and changed to Vancian spellcasting”. At that point, you’re basically playing your own system where the stats and classes are inspired by D&D5e, but nobody would call that “D&D5e but with house rules/homebrew”. There’s more stuff that isn’t D&D5e than that is.
This is exactly the kind of thing that people get annoyed at D&D people about, just sort of in reverse; D&D people run different settings with a 5e ruleset and call it a “new system”. You’re running a system’s setting with a different system and calling it “the same system”. There’s absolutely nothing wrong with pasting Shadowrun’s setting onto a new system, but if I run a campaign in Shadowrun’s world but I replace the mechanics entirely with D&D5e, I’m not running Shadowrun. I’m running D&D5e.
I think at this point I need to ask you to take a step back and remember where this conversation started.
I opened by saying that Shadowrun is not an entry-level system because the rules are hard to understand. What it seems you did was take me saying “Shadowrun is not an entry-level TTRPG” and append “setting” to that, which is ironic given this post.
I never meant to imply that the setting was hard to understand. It’s the rules that were the problem, and I apologize if that wasn’t clear enough. But from my perspective, I said “The rules are hard for a new player to understand” and - again, from my perspective - your response was more or less “The rules are fine if you change all the rules”. So you can imagine why I was blunt in my responses. This whole thing has been in the context of the rules system from the start, so yes, I am focused on the rules at the moment.
But I do stand by the fact that Shadowrun’s setting with different rules is not “running Shadowrun” the same way running a D&D5e ruleset in a modern setting is still “Running 5e”. It’s the rules that matter in the context of statements like these, not the setting. You don’t say “I’m running Forgotten Realms” You say “I’m running D&D.” Sure, sometimes you specify modules but those modules are known to exist in a specific system so saying “I’m running Rime of the Frostmaiden 5e” is redundant. What you’re doing is “Running [system] with Shadowrun’s setting” or perhaps “Running Shadowrun’s setting with another system.” The distinction is still important, and anyone who reads “I’m running Shadowrun but I changed all the rules” will likely interpret that in their heads to mean “Shadowrun['s setting] with different rules” anyway.
Or TL:DR; you “Run” rulesets, and your campaign takes place in a setting.