That's a mighty big blanket statement, calling huge corporations with tens of thousands of employees "unethical"!
Some things I might consider to be unethical have been done by some major corporations. Does that mean, by definition, the whole corporation is unethical?
When you look at the problem of illegal drugs, who do you blame? The coca or poppy farmers? The cartels? The disadvantaged youth who deal them on the street? Or the people who fuel the whole economics of the illegal drug trade by their insatiable demand? Same with fossil fuels: who do you blame when a well blows out or a tanker runs aground: the people who screwed up drilling the well or piloting the tanker? The people who pumped the product in the tanker from the ground? Or the people consuming the product as fast as it can be produced?
I don't personally like Exxon's stand on global warming, but I certainly understand why it is consistent with their business interest to hold it. I also understand why they do everything (legal) in their power to make that point of view known and to have it spread to as many others as possible, especially to people in power. But the only way I could possibly view Exxon itself as "unethical" on that point, i.e. because this corporation holds a point of view which maximizes their short- term profit while leaving a giant hole for future generations to attempt to fill in, would be to have a totally naïve perspective on what a corporation is, or should be.
A corporation isn't a "person", it's an algorithm. Its goal is to maximize profit and shareholder value for the people who own it. It has no "ethics". It should never, ever, be expected to hold any values other than those which can be defined in legal terms. In fact, if the management of a corporation attempt, as they often do, to spend the corporation's money toward values other than those fundamental to the corporation, the shareholders should be there to question why it is being done.
If you're realistic about what corporations are, and aren't, then you'll understand how important it is to have a democratic government and the rule of law in place everywhere that corporations carry out their business. Where we are in trouble is when the power of corporations intrudes into, and corrupts and undermines, the functioning of government. And we should always expect that if a corporation can do so, it will, in order to do what its algorithm tells it to do to the greatest extent possible.
If what you're asking is the simpler question of whether or not you should work for organizations whose business model offends your view of a) what's good for the world or b) what you think will make a good future for the company and hence permit it to continue to provide you with employment, then that's a dead easy one. When you have the choice, you make the choice. When the choice is between working against your ideals or going hungry, it's a much harder question to answer.