That's not the end of the sentence, and there's no comma to separate the rest as a separate clause, and, there IS a clause that clearly limits it.
If the 15th amendment means what you say, the 19th should be completely unnecessary, as would the 23rd, 24th, and 26th. And even with those, we don't let citizens under 18 vote, or felons in some states.
Don't forget that the idea that every citizen would vote in every election didn't exist in 1788; it was generally understood that states could come up with any method they wanted to choose electoral college delegates. A state could literally decide that the governor or state senate could pick who the state was voting for, without a state election.
Compare that to the 2nd amendment, which has no qualifiers at all: "... the right of the people to keep and bear arms, shall not be infringed." (period, full stop)
Or compare it to the 1st amendment, which also has no qualifiers.
Or to the 4th amendment, which *does* have qualifiers.
Clearly the qualifiers (or lack of) matter.