In this scenario, it's less about the damage you can do to the company and more about the damage you avoid doing to yourself.
Integrity is something only you can define for yourself. If you're fine with it, do what you want and live with the consequences (or lack thereof).
To your example, I don't eat Chick-fil-A, and I don't shop at hobby lobby. There's something to be said for "there's no ethical consumption under capitalism" but those two companies in particular, I find repulsive, even though they remain incredibly popular. I know my boycott doesn't impact them, nor does it stop anyone else from supporting them, but I feel dirty when I shop there, so I do not.
Wonderful in theory, but in practice it's a dumpster fire. Quick, mainstreamm-acceptable takes are incentived, and nuanced, alternative viewpoints are nearly impossible.
If it were all for hobby stuff, it would be fine, but when this is how most people get their news, it's not good.
The reason we haven't had a redo of the French revolution, despite having a more fucked up tax system and higher economic disparities, is because the massively rich wised up. They don't go in public very much.
Private parties, private clubs, etc. if they do anything in public, it's a minimum of several hundred dollars per person so that normies can't afford to even look that direction.
They've already got a better system than Hitler could have every hoped for: normal prison.
The US has the largest prison population per capita, plus migrant holding facilities, plus juvenile holding facilities.
All they need to do is capture the presidency and keep at least one chamber of Congress, and they can just expand the existing laws to target their enemies. The facilities are already in operation, they just need an excuse to grab the people they don't like.
If they advocate attacking a black person, they know they'll get immediate blowback.
Attacking the "race traitor" is a level of obfuscation. There are more people who believe that races shouldn't mix than believe that people of color should be targeted directly.
It's like water - they're going to find the path of least resistance and pick up as many as they can along the way.
This is a good idea in theory, but it doesn't really hold up when you look at what we ask reps to do.
They have to maintain two households, basically, and have a lot of travel expenses.
State legislatures are a great sandbox to review how pay impacts the folks who can afford to hold seats. Turns out, the less they're paid, the more likely they are to be independently wealthy. You will never "show them what it's like" to be poor by paying them less - you'll just ensure that actual normal people can't afford to take the position.
I think it was Maine that had a fully volunteer legislature? And had the richest legislature ever.
Ultimately, this is another problem of America trying to retain an agricultural mindset (part time legislature so that everyone could go home to farm), despite the world having changed.
There are no empty spots for them to claim, and I highly doubt you can draw a line anywhere that would work. They tried that with India/Pakistan and it was an absolute cluster.
This isn't like the civil war where it was regional. This is a lifestyle divide.
You need to stop giving regressives the benefit of the doubt. They will couch their rhetoric in as much plausible deniability as you're willing to extend them, exactly so that you'll go into the comments and carry water for them.
You and I both know beyond a shadow of a doubt that this will be prime fodder for AM talk radio, pulpits, and other bastions of the culture war. They are out there right now saying, "This is sad, but the boy [sic] was confused and was groomed by society." Framing it as grooming, dead naming, etc. is all a way for them to muddy the waters and poison the well. If it isn't blood libel, it's a single step away. Here's one example, I am sure you can find more if you look: https://twitter.com/JermontII
It was their children, engaging in terrorism they support (this is the natural consequence of the rhetoric they spew against LGBTQ+ people), against someone they consider subhuman.
If they haven't expressed their displeasure yet yet, it's because they're waiting for Fox to tell them which spin it needs to be "acceptable."
Remember Kyle Rittenhouse? The judge literally posed for pictures with him, and they turned him into a media darling and will probably run him for office if he can stay relevant and out of jail for a few more years.
As with all things regressive, their whole truck is to treat their own viewpoint as a default state, and then try to force everyone else to argue around it, which allows them to steer the discussion and eventual outcome.
When they're headed off on one avenue they pivot, but this is the consistent direction of almost all regressive talking points.
Not going to lie, my first thought was to wonder whether and how they controlled for this.
But I took a step back and reminded myself that REDLINING HAPPENED. Well into the modern day. It was only outlawed in 1968, and there's evidence that banks continued to do it through the 70s.
It's absolutely no surprise that there are still disparities, and I would be further unsurprised to find out that the deciding factor was zip code.
In this scenario, it's less about the damage you can do to the company and more about the damage you avoid doing to yourself.
Integrity is something only you can define for yourself. If you're fine with it, do what you want and live with the consequences (or lack thereof).
To your example, I don't eat Chick-fil-A, and I don't shop at hobby lobby. There's something to be said for "there's no ethical consumption under capitalism" but those two companies in particular, I find repulsive, even though they remain incredibly popular. I know my boycott doesn't impact them, nor does it stop anyone else from supporting them, but I feel dirty when I shop there, so I do not.