I've been a Stack Exchange user for over five years, and a moderator on one Stack Exchange site for three and a half of those years. In that time, there have been occasions when I've entertained the idea of quitting, either leaving SE altogether (before my moderatorship) or at least resigning as a moderator. Right now, many users and moderators are stuck on the horns of a dilemma: they disagree with recent directions or decisions taken by the Stack Exchange company, but they still feel some loyalty to their communities and some of the people within. Some have already made their decisions, quitting or continuing, but others are still torn. I'm hoping that this post may help them.
How do you see your role on the site?
This is mostly for moderators: I've seen the moderator role described as representing SO Inc to the sites and communities, or representing the sites and communities to SO Inc. Are you the face of company policy, enforcing it as the moderator rules require, or are you the face of your site's community, fast-tracking their issues and concerns to the company for resolution? The same question can hold for non-moderator contributors: do you see yourself as helping to build and refine the company's stock of knowledge, or as creating something valuable for other people on the internet?
If you feel that you're mostly helping SO Inc with their stuff, at the expense of your own time, then it may be time to quit if you can no longer support the company. If you feel you're part of a better cause that you care about, with the company being mostly marginal to your life, then you may be able to continue regardless of your feelings about SO Inc.
Are you safe?
The more prominent you are on the site or network (e.g. as a moderator), the bigger a target you become. Personally I've always taken pains to keep my SE persona completely separate from my real life, for a number of interconnected reasons. Your actions on-site might lead you to be targeted by anyone, from random trolls to SO Inc itself. Make sure that if someone wants to find you and take revenge, or if you appear in the press in relation to some SE drama, then it's only your SE persona that takes the hit. I don't particularly care if "Rand al'Thor" gets branded a scumbag all over the Internet; I could mostly just continue with my life.
SE is not your "safe space."
Or rather, don't rely on it too much. It should of course be a space where everyone is welcome to participate and interact, regardless of who they are, but it's also owned and run by people with their own agenda. Don't put too much of yourself into this place, because it may not last forever and certainly won't stay the same forever. For example, if you feel safe to express your political views here now, that safety may not last. SO Inc is lending us the use of its platform, and it reserves the right to terminate stuff it doesn't want.
To take a deliberately extreme example, a follower of Nazism could be a perfectly good SE contributor as long as they don't express their racist views here. SE is a "safe space" for them to interact and share their knowledge, but not to share everything they think. You, the person reading this - I'll bet you're not a Nazi, but I'm sure you have some views which differ from those which SO Inc has or will have in the future. Even if they seem irrelevant to you, those views could become hot-button topics here in the future. Be careful, especially about sharing too much of yourself.
(This point may work differently on a few network sites, like Politics or Interpersonal Skills. But for the most part, sharing personal or political views isn't strictly necessary for participation, and you can decide how much you want to do that and where to draw the line.)
Don't get emotionally attached to the company.
Some people seem to have lost a lot of trust in SO Inc through its recent actions; they expected better. Some of them may still remember the cosy startup days when employees might regularly hang out in normal chatrooms and a moderator might know half of the employees quite well. I wasn't around in those days, and I never invested much trust in the company as a whole. Specific community members, sure. Even specific company employees, or whole subcommunities on the SE network, might be worthy of trust or emotional attachment. But don't be surprised if the company takes some action you'd never have expected. We don't know what goes on up there, and we never will (unless we also get hired).
Most importantly, don't stay because you "believe in SO Inc". Staying because you have a community that you care about, or because you want to continue helping and having a positive impact on a site you're invested in - nothing wrong with that. But if you stay because you trust Stack Exchange itself, you're going to end up disappointed, one way or another. They can't satisfy anybody all the time, and it's not even their goal to satisfy us the community, so it's hardly surprising that they'll fail in that.
Try to make your decision based on what you know - including your feelings, e.g. attachment to this or that subcommunity for such-and-such reasons, since that's an objective fact too - but not based on excessive optimism or cynicism. Don't fall into the twin traps of thinking the company cares about looking after you or thinking the company has become some evil dystopic Big Brother. Individual people within the company may well be moral people who want to take care of you, but they may not be the ones calling the shots. The company as a whole will make objective decisions based on what's best for it (which may include nurturing the community in certain ways, but maybe not as much as you'd like or not in ways that you'd agree with) - try to do the same.
In the end, you have to weigh the positives against the negatives. For most people, I imagine the positives will include some subcommunity or subset of curated content that you care about for its own sake, while the negatives will include the fact that this platform is hosted by a company that you may no longer trust or support. Those are good positives and negatives to have, but I can't make that decision for anyone except myself. All I can do is try to ask the right questions, guide your thoughts to where you'll be more able to make that decision.