Perhaps you're not aware, but a republic is a form of democracy. The term "democracy" comes from Attic Greek, and is a combination of two words: Demos means "people" and Kratos means "power." Put simply, the basic idea is that the people ruled have political power. Democracy (in any form) stands in sharp contrast to oligarchy (rule by few, Oligoi=few, Arkos=ruler), monarchy (rule by one, Monos=one), or other forms of government in which the people ruled have no, or very little, political power. In a direct democracy, every citizen with voting rights votes on every decision (or at least every citizen with franchise is allowed to vote on every decision). A republic is just a form of indirect democracy, in which the people periodically vote on individuals to represent them. Such form of government still counts as a democracy because ordinary citizens have substantial political power--namely, the power to vote on representatives, and usually also on ballot initiatives or other such direct-voting questions.
When the OP says the U.S. is no longer a democracy, he is saying that, by various means, political power that is ostensibly or legally in the hands of the people has been removed or undermined--as it clearly has. Gerrymandering, especially to the degree we see it at work in this country, causes rule by a minority--which tends towards oligarchy. Historically, oligarchies have been hostile, and quite bad pragmatically-speaking, for individual rights. Thus, when someone says that democracy in the United States in on the decline, and someone else comes along and says "the U.S. has never been a democracy. It's a republic," that person is (usually unwittingly) aligning themselves with various political forces that want to get rid of things like freedom of speech, freedom of religion, right to bear arms, freedom from unreasonable search and seizure, and so on.
Rather strangely, it always seems to be right-wingers--people who insist they are for individual rights and freedoms, who try to downplay the anti-democratic forces at work in our country and hence assist those who would like to take power from citizens--often at least one of them can be counted-upon to make the remark you've made here, in an attempt to distract from the issue at hand.
Any state that is not a democracy is not a republic either. Conversely, if a state is a republic, it is, by very virtue of being a republic, a democracy.