If you are on the fence enough to ask here, don't quit immediately and instead just start interviewing elsewhere now. Once you have some solid offers lined up, you can make a more informed decision.
In general a large corporation is -- surprise surprise -- going to be made up of a lot of people. Some of them are going to be really passionate about doing the right thing, some of them will be happy to do what it takes to get ahead, and a lot of them are just going to want to do their job, get paid, and not worry too hard about the bigger picture. It can feel bad to be at the big evil and feel like you're being corrupted by being a part of it, but you always have the option to do what you think is right. You can stay there, work hard, and push back against the culture and attitudes you think improper. Maybe you'll make a difference. Maybe you'll give up. Maybe you'll try hard but no one will listen, and meanwhile your hard work will benefit the wrong people. Maybe you'll get fired after people get tired of you telling them how bad they are or after you refuse to do something that crosses the line.
Does this actually work for people? My experience interviewing for software engineering roles is that it's a time consuming and tedious process. I can't imagine juggling a full time job while interviewing with more than one company at a time.
My one experience doing it has only involved one job change/interview/offer, so I'm not sure what the typical experience is.
After I grew dissatisfied with my first job out of college, partially because I'd just been there five years and wanted to try something else, partially for ethical reasons (the new owners were hosting fundraisers for Jenny McCarthy), I sent resumes to three companies, got a callback from one, did a phone screen, took a day off work for the interview, and then got the offer a few weeks later. Gave three weeks notice, took a month off, was at a new job about three months after I first decided to leave the old.
In general a large corporation is -- surprise surprise -- going to be made up of a lot of people. Some of them are going to be really passionate about doing the right thing, some of them will be happy to do what it takes to get ahead, and a lot of them are just going to want to do their job, get paid, and not worry too hard about the bigger picture. It can feel bad to be at the big evil and feel like you're being corrupted by being a part of it, but you always have the option to do what you think is right. You can stay there, work hard, and push back against the culture and attitudes you think improper. Maybe you'll make a difference. Maybe you'll give up. Maybe you'll try hard but no one will listen, and meanwhile your hard work will benefit the wrong people. Maybe you'll get fired after people get tired of you telling them how bad they are or after you refuse to do something that crosses the line.