If i understand this correctly (and that remains to be seen as only recently have i managed to deal with this properly), you get influenced depending on the difference of level knowledge from your culture agains another civ.
Levels are :
Unknown (Tourism < 10% Culture)
Exotic (Tourism ≥ 10% Culture)
Familiar (Tourism ≥ 30% Culture)
Popular (Tourism ≥ 60% Culture)
Influential (Tourism ≥ 100% Culture)
Dominant (Tourism ≥ 200% Culture)
So, say all tourism of all civs makes it that everyone's culture is "unknown" to any other civ. Then, no one will suffer any impact from ideologies.
Now, if one civilization that has a different ideology than yours has its culture being "exotic" with you (so his overall tourism reached 10% of your overall culture), and your culture is still "unknown" to that civilization. Then you'll get 1 level of influence on your civilization which is symbolized by an icon from the ideology (hammer\sword\torch thingies) when you put your mouse over the public opinion status in the tourism\culture overall screen.
If it's two civilization from the same ideology that are exotic when you're still unknow to both of them. You get 2 levels of influence.
Then depending on how much level of influence you're under from the different ideologies different than yours, you suffer penalties as follow :
Dissidents - 1 Level Influence difference total. Suffer Unhappiness equal to the greater of 1 per City or 1 per 10 Population.
Civil Resistance - 3 Levels Influence difference total. Suffer Unhappiness equal to the greater of 2 per City or 1 per 5 Population.
Revolutionary Wave - 5+ Levels influence difference total. Suffer Unhappiness equal to the greater of 4 per city or 1 per 3 Population.
So it's all about the difference in levels of consideration of your culture\tourism in AIs civs vs level of consideration of AIs culture in yours.
World ideology from the world congress seems to act as a "free virtual level" of culture popularity for all civs with that ideology. So an unknow culture with World Ideology will act as an exotic one. An exotic one as a familiar.etc..
I take all this mostly from my most recent games. And i think they make a good example. Especially the one i did with Arabia on DCL 24.
Here's how it went as an example
I had produced enough tourism to be exotic with 6 of eight AIs. 3 had took order with only germany being exotic over me being unknown to them. France took autocracy and was exotic over me being unknown to them.
So i'm at : 1 Level of influence from Order (germany) and 1 from Autocracy (France) = 2 levels of influence from other Ideologies = Dissidents
I picked liberty and suffered 2 level 1 penalty which made happiness an issue but still allowing me to keep it over 7/8. I immediatly started to switch my tourism toward France and Germany (trade routes, paying 4/5 GPT to buy their open borders, even used a diplomat with France as i was buying votes for World Religion).
I managed to get exotic with germany quite fast (wasnt far from the 10% mark) which made all unhappiness from order go away. (as all order AIs were exotic to me or lower and none were more than exotic to me)
So i'm at : Level 1 of influence from Autocracy (France) = Still dissidents
Then, World Religion passed, with World Ideology for Order as well. The blow was brutal (got a 2 "hammer" symbol in the unhappiness culture screen from order) as germany and the other AI (america i think) that were exotic to me started acting like they were familiar. So 2 level 1 penalty make it a lvl 2 penalty. I'm at -4 happinness from something like 10/15.
I'm at : 2 levels of influence from Order (germany + america) and 1 level of influence from Autocracy (France) = 3 levels of influence = civil resistance
I instantly decided to abrogate World ideology for Order (cost me a LOT of money and hate) and decided to focus my tourism even more on France (as trying to reach familiar toward germany and america would took too long). I bulbed 2 musicians in France borders, and world ideology boosted my cap tourism output. I managed to reach exotic toward him and took off the level 1 penalty from autocracy.
I'm at : 2 levels of influence from Order (germany + america) = back to dissidents
Finally, i managed to get the abrogation of World Ideology for Order. Which made all penalty disappeared as America and Germany culture got back to act as exotic only.
I'm at : 0 level of influence from other civ = satisfied = No penaly at all.
EDIT : as people mentionned in the next posts. The level of influence from civs who share the same ideology as you will act as a defense.
Example :
You : Order \ Unknown culture to all civs
America : Order \ Familiar culture toward you.
Egypt : Liberty \ Exotic culture toward you
Mongols : Liberty (lol) \ Exotic culture toward you
Siam : Autocracy (lol again) \ Exotic culture toward you
Poland : Autocracy \ unknown toward you (lol, but that happens right)
So, with that setup, you have 3 negative level of influence from Liberty (2) and Autocracy (1).
=> That should put you in "civil resistance" status
But, America is familiar with you, so that equals to 2 level of influence "against" you. But in a positive way as it is the same ideology you picked.
=> That negates 2 of the other ideologies level of influences. So you're left with just one negative level of influence
Poland is unknow toward you, and you toward them so that does nothing.
Bottom line: you only have 1 level of negative influence left. So you're "just" in Dissidents status.
I hope that helped, and i hope people will correct parts where i'm wrong (there must be some no doubt). And if you want more information, check out that video :
Marbozir has what in my opinion is a very clear explanation
here.