It depends on what your frame of reference for diversity is.

Of course within states, nationalism has made these states less diverse, as borders were deliberately drawn to minimise diversity (as in the post WW1 state creation) and forced migration was sometimes used to aid this (e.g. the Greek-Turkish population exchange). Furthermore the nation building processes (e.g. universal education in the national language) can have the effect of removing diversity (e.g. in France where French was taught and not Breton, Occitan etc, see Eugen Weber's 'Peasants into Frenchmen').

However sometimes it's difficult to disentangle nationalism from the other processes of modernity of which it is a part. E.g. increased speed of communication and internal labour migration are also contributors to the reduction in diversity (e.g. regional languages)

If we're talking about diversity of states, then compared to the age of empires preceding that of nationalism, then nationalism made the world more diverse, so you had many states emerging from a few empires (Ottoman, Germany, Austria-Hungary, Russian) in pre-ww1 Europe, and a similar process taking place in Africa during decolonisation.

Overall, if we try and take an objective definition of diversity, like say number of languages spoken per 1000 square km, then the processes of modernity, of which nationalism was one expression, certainly reduced diversity. A good question is whether if the processes of modernity had taken place but in a very anti-national framework (say if the Holy Roman Empire controlled all of Europe and drove it forward to modernisation) then if there would have been a similar reduction in diversity.