If these people have genuinely become naturalized citizens of the country, and fulfil the laws of that country, then they are allowed to play. Assuming that they also fulfil other FIFA requirements such as not having played for another country. It's not so different from what the Gulf countries do, or what the USA has done in the past.
Or are you saying that they aren't genuine citizens?
They are obviously genuine (otherwise of course they wouldn't be allowed to play
), but some cases do make you question the methods a little. In Europe Poland appear to be one of the worst 'offenders', Nigerian-born Emmanuel Olisidebe played in the 2002 FIFA World Cup (international debut in 2000) after just 3 years in Poland, while in 2008 Roger Guerreiro (born in Brazil) played in the Euros after less than 2 years of residency (the Polish authorities admit to having 'fast-tracked' his application in time for the summer).
For the record, both players scored in their respective tournaments, so if the locals had any issues at the naturalised players they were probably quickly forgotten, just as the Equatorial Guinea squad was presumably warmly-recieved in 2011 (women's) and 2012 (men's) for their achievements.
It depends on the country, though, the Home Nations have their 'gentleman's agreement' that has stopped naturalised players from being called-up, even if players such as Manuel Almunia and Nacho Novo are eligible for England/Scotland respectively.