Modern democratic societies try to incorporate more tolerance of cultural diversity, but there are aspects of many cultures that are antithetical to this goal.
The rise of trade over the centuries has meant that many have had to adapt to the ways of other cultures, or at least tolerate them. If the trade has been too exploitative in a country, its citizens have sometimes had to revolt, leading to much intolerance and violence. Eventually, some point of balance occurs, though it usually favours the most forceful.
Force, violence and suppression have long been the tools of rulers to make their subjects conform, so a lot of the culture of their societies have institutionalised those aspects over a long period. Those in the culture have come to expect certain classes of people to conform to social norms that maintain the current power structure. Those norms have often been framed within the lore of the dominant religion as it suits the leaders in their quest to control their population's thinking and behaviour.
As modern democracies try to aspire to transcend their pasts of colonial and domestic violence, they have also tried to be more accommodating of other cultures. Part of modern democratic thought is to protect citizens from violence, not just by individuals, but by institutions as well. We have seen investigations from around the world of child abuse by religious and government institutions, especially against racial minorities and the poor. Alongside these discoveries is the ever-growing acknowledgement of domestic violence, mainly against women and children.
So there is a desire to be more tolerant of cultural traditions while dealing with domestic violence embedded into countries' own cultures. The problem is that almost every culture has forcefully dominated those who were weakest in their societies, so the criteria for improving our societies is to weed out those aspects relying upon discrimination and violence, regardless of the cultural history behind them. This is the writing on the wall for all societies and cultures, which means that all aspects of any culture needs to be examined for whether those aspects should continue to be supported.
Many may think that the whole of their culture should be respected, but if the culture that they have moved into is examining itself for embedded violence and suppression, any imported cultures should and must be examined as well. No culture has ever remained the same, except if it wasn't invaded, so cultural identity consists of a lot of ingrained habits developed over time and modified by whomever took over ruling the show. While some may harken back to a culture's so-called heyday, those who were subject to its abuses do not.
A society is the sum of all its cultural influences, so all participating cultures must be part of the evolving to a more tolerant society. Pretending that a culture can or should be immune to changes going on around it is unrealistic. Expecting tolerance but offering none is unfair and discriminatory. For many, their path has been an escape from what their home culture has become, so while they may prefer to maintain what they had before the changes, the reality is that the culture in their former homeland was failing to keep itself afloat among its challenges.
Many of those same challenges are worldwide, so their new home is no escape from them. The world does not sit still, and cultures that still support violence and repression will not survive in a world that is forced to confront the violence of the past and all the destruction and suffering that has caused, to people and the planet. People cannot flee from violence but expect to be allowed to take it with them to a new country, as that will only lead to more violence to flee from.
The climate crisis is leading to much migration and will continue to do so into the future. Migration challenges cultures to adapt and let go of what doesn't translate into their new environment. In the past, migrant communities have been ostracised and suppressed and so only had their language and culture to keep them afloat, eventually finding their own strength to rise above their suppression. Even though many countries are having issues with too many destitute migrants, they largely try to adapt to their presence and provide support.
The price of that is that the new levels of interaction require migrants to also adapt a lot faster than they have in the past. Any embedded violence or repressive aspects of their cultures get brought to light more quickly, requiring them to let go of them or face criminal penalties. The world is changing to be freer, at least in the thinking, so anything that stands in the way will eventually be uprooted. Some may try to change that destiny, but it cannot be stopped.