Quick question, does all tourism of that opposing ideology go against your culture together or seperate?
For example is it like this (Your Japan and went with Freedom and the other nations went with Order)
Russia Vs Japan (60 tourism a turn) England vs Japan (40 tourism a turn) or Russia and England vs Japan (100 tourism a turn)
I think it's really a bit more complicated than that.
In the first place influence gain has nothing to do with ideologies and it is separate per each civs.
Unhappiness due to ideologies of civs that are influential on you is a whole different matter and depends on many factors.
In the first place it isn't raw tourism that matters but the discrepancy in influence gain.
So if you are gaining influence faster than they are gaining influence on you they are getting unhappy and viceversa. This means that culture is included in the picture.
The other point to consider is proximity. Basically this works like religion, the more someone is closer to you the more their influence will affect your happiness.
So basically yes, more civs of opposing ideology will have a bigger impact on your happiness but only if they are close to you.
If the second civ is on the other side of the planet, though, it won't change a thing.
The important thing to remember is that influence is not directly correlated to your happiness penalties. One could have an enormous influence over you but not affect your citizens because it's far.
You can actually have a grasp of who is actually affecting you that way by hovering the mouse on your "unhappiness" in the cultural screen. That is represented by the number of ideology icons, and you will also know who is giving you more of those icons.