The belief that rich people will be able to ride this one out is a huge part of the problem. No matter how deep your bunker, no matter how many acres of land you own, extreme weather will make all of it worthless.
The climate change may easily cause large scale international conflict or fights over resources at national level, but the distance between places without capacity to handle the weather and the better-off areas generally are thousands of miles and an ocean, and the parties to any conflict would be neighboring communities of many millions of people each - I mean, this discussion is about "what will happen to the population of current Bangladesh, and what effect that will have on neighboring countries" not about what will happen for few rich people in USA against their literal neighbors from the same state and county.
I fully expect that the wealthy countries can handle some internal displacement due to e.g. sea level rise without mass violence and a general breakdown of internal order - people having to abandon coastal properties in Florida would cause economic woes and internal political pressure to Do Something (not necessarily constructive), not cause the displaced Florida men to form large uncontested gangs roaming the Midwest looking for bunkers to loot.