Speaking about word choice for a moment, the idea of the “grant” of a right is not quite right. It is the typical way of discussing these rights, however, it may be more accurate to say “The identification of a right critical to good governance to an individual and recognized formally through the process of Amending the Constitution.” It is easier and accurate enough to say “grant,” so that will be used through this discussion.
Back to the subject. There is now a right granted to the individual, such as the right to the freedom of speech or the right to a speedy trial. The question now becomes from whom does the right protect? Another way to look at this is these rights give protections to an individual, who is the individual protected from? The short answer is the government. The slightly longer answer is from the Federal Government unless there has been some action, such as being included in the Amendment or by the Supreme Court, to extend the reach o the Amendment to the States.
This is the concept which trips people up the most. We don’t have “Freedom of Speech.” As American Citizens, we are not free to say whatever we want in whatever medium we want. Instead, when we have the ability to speak, the government cannot limit that speech. A protest is speech protected from prosecution from the government. A cartoon mocking the president is protected speech which is insulated from government action.
However, and this is an important however, there is no such limitation on private parties. A business can fire an employee who stumps for a political candidate the business doesn’t like. A person who throws a party or event can throw another individual out for any reason, regardless of the freedom of assembly. There is no universal freedom of religion and a religious organization can remain solely for individuals who agree with such religion. Nor is the universal protection from unreasonable searches and seizures. These are all situations where an individual can do something where the government would be prevented from performing the sam action.
The Constitution gives and limits the powers of Government. That is the extent of its reach. That is not to say it is ineffectual or unimportant. However, the key is and should be that the Amendments and the Constitution describes the form and ability of the government. Other individuals and citizens are protected from their government, not each other.