Why did people support The Communist Manifesto?
Not sure if there were any specific "people" supporting it, but there are communist countries out there and I'm guessing the things in the manifesto was supported by someone or a group of people to make a country communist. I'm lost sorry!
First of all, please realize that no country became communist until 1917, which was almost 70 years after The Communist Manifesto was published.
In general, the people who came to agree with the ideas of Marx and Engels were those who were being hurt by capitalism. They were mostly the workers who had a hard life under the capitalist system.
Remember, Marx and Engels are essentially saying that capitalism is a system in which the bourgeoisie, the owners of the means of production, abuse the workers and steal from them. They argue that the workers should overthrow the upper class and take control of the means of production and of the whole society.
Once you remember that, you will be able to see why some people would support these ideas. Those who felt that they were being abused by capitalism would be likely to support an argument that agrees with them and tells them that they ought to be the ones in control of the workplace and the society.