If you are outside a company, you really do not know how that company works, unless you study it for a long time, and even then you are probably wrong on significant issues unless you work there every day for a while, usually several years. As time goes by, you will start to see similarities between the different corporate cultures, but ultimately each company and project has (or may have) its own individual insanity.
There are always politics, every project has them and every company has them, although they can differ wildly in their style and intensity. But you, as a consultant, are at best an aide to one of the players, you are not a player yourself and you should never forget it. If anyone is expendable, you are.
These kinds of projects are pretty much all involving for the consultant, they involve all your time and energy, and you may have very little idea from week to week where the project is going and how much of your time they are going to need. All you can do is put the rest of your life on hold, and do what you and your client think is right on a day by day basis. They do not know how much of your time they will need, nor do they know how long you will be working for them.
Do not think that by contributing to a project at the beginning, when usually that there is less time or money then there is ultimately, that you will be able to participate in the project when the real deadlines and budgets are revealed. It doesn't work that way.
I like to describe the differences metaphorically by asking the following question which actually does not have a right or wrong answer, it is all a matter of personal preference: "You are a consultant to the captain of the Titanic. Would you rather be a consultant to the captain of the Titanic before it hits the iceberg or after it hits the iceberg?"
Although they have hired you to advise them in an area where you have considerable knowledge and experience, and even when they are paying you good money to get your ideas, very often they want to do things their way. At the end of the day, in fact, it is their project and not yours. At some point if you keep whining about something they don't want to do, or try to keep them from doing something they do want to do, they will just get rid of you. Ultimately they are going to do it their way.