In a global sense, whites are not a majority. It's something to be considered if you are going to discourage whites from claiming pride, as national boundaries are becoming less meaningful.
I am not proud of my culture so much as I am happy, but it seems hypocritical to support the idea of pride for one group and not another. Sure, it may be practical now, but consider if things change radically in the future. Hispanics or some other minority are now for the most part the ones in power. What is now considered a healthy outlet for minorities to motivate themselves, could be fostered into an unhealthy form of bigotry if roles are reversed.
Now I wouldn't forbid the right of any group to claim they are proud of their race, as it would be immoral, but I don't think it is a healthy line of thinking.
I think the best way to deal with supporters of white pride is to simply let them be as long as they are not violating anyone's rights. Trying to suppress them only fuels their idea they are being persecuted.