Yes, diversity can be accommodated in democracy, and democracy is often accommodated well, because in a democracy, politicians need to make compromises in order to reach enough of a consensus to get anything done. With a majority vote, people need to be in agreement to take action. This makes people work together to find diverse solutions.
In a democracy there is room for everyone to state their opinion and be represented in some way or another. Ideally in a democracy, we would all choose where our tax dollars would go directly. For example, religious people could have tax dollars go toward funding public religious schools and skateboarders could put their taxes toward skate parks and musicians could use there taxes to fund music programs in public or in schools. Anyone could put their money toward anything they want, and while much of it would necessarily be diverted, for example if one person has one idea and no one else supported it, then the person would have to choose from a host of ideas they could support. If we had a true Democracy, we would not have war. Democracy is the best government for diversity.
Divided by area, age, gender, intelligence, race, culture, religion, and beliefs, how can a democracy fairly represent all these different types of people, especially when each of these types of people represents a large portion of the vote?
These people who add "diversification" come to democratic countries to be fairly treated, their idea of "fair". Assimilation is only skin deep as these people have come from a culture and identity that does not necessarily (but can) coincide with the beliefs that helped make and sustain democracy in the first place.
The idea that a 'melting pot' adds to a country is false, it adds dissidence, because everyone is chasing the status quo, or their rendition of it.. This divides people on a basic level, through race, religion..Etc.
Divided by area, by intelligence, by culture, by language, religion, race. Not all people share the beliefs that helped to create and nurse democracy through its infancy to its dominance in the world stage, so why introduce people who, in their native land or country, didn't come from a culture or form of government that shares the same values as the democracy they are moving into? They come for money, their values won't change, and in doing so the people divide themselves into smaller denominations which makes the vote less important.