I don't think they will go extinct. Blue eyes/light hair/light skin are a mutation from a single individual which was selected for over thousands of years against millions of others. Given there are many whites on earth across all continents, it is unlikely that whites will go extinct, assuming their fair features continue to be sexually selected, by all races, across different continents. For whites to die out there would need to be a cultural shift wherein whites do not set the beauty standards and aren't sexually selected for. This seems unlikely, as, if you as a male go to Asian / Latin American countries, there is a continued preference for lighter features. It would also require all non whites out competing white birth rates. While this is true globally, in multi cultural countries, especially white minority countries, persecution of whites increase and white collectivsation increases, meaning white birth rates increase. Thus, ultimately what would need to happen for whites to go extinct over 200 years would be a global and systematic attack against white livelihood for a prolonged period of time, by all other races across all regions of the world (socially, physical, biological, metaphysical warfare). This seems unlikely as it would operate on the assumption that India / Asian / Latin American demographics would decide to physically extinguish whites. It ignores the fact that many of those regions elites are half white or in some cases, fully white themselves, lowering the probability of systematic attack on white people. It also ignores the reality of polygenic risk scoring and CRSPR technology where countries like India and China, which aren't infected by moral syphilis, have a preponderance for selecting for 'morally reprehensible' traits, according to the Western perspective, such as light features, light eyes, light hair, light skin, intelligenge and height. As this technology becomes cheaper, the effects will socially and demographic effects grow exponentially. If anything, the aforementioned logic ensures that whites will continue to survive.