Is it? If so, examples?
Causation without Correlation is Possible?

Let
y = bx + u
where y and x are demeaned random variables, u is a random variable, and b is a scalar. Then the causal effect of x on y is b, and
Cov(x, y) = bV(x) + Cov(x, u).
Suppose Cov(x, u) = bV(x). Then for any nonzero b, x causes y but x and y are uncorrelated.

Suppose every time a bigger kid steals a dollar from you, yo moma decides to compensate you for it and gives you one dollar back. Your nerdy friend looks at the correlation between $ in your wallet and $ stolen from you and finds no correlation. Nevertheless, there is a clear causation between stealing money from you and how much money you have.

Suppose a side effect of birth control pills is that they increase the risk of thrombosis. And that pregnancy itself increases the risk of thrombosis. Naturally, the pills reduce the chance of pregnancy.
If the pathways cancel out, then you have a case of causation without correlation.
Correlation is a linear relationship in means. There are plenty of causal relationship that could be nonlinear, causing the correlation to be 0.
I assume OP is talking about conditional independence?

Correlation is a linear relationship in means. There are plenty of causal relationship that could be nonlinear, causing the correlation to be 0.
Lolwut? Correlation does not require linearity. It's just a simplifying assumption used in some tests.Corr(X,Y) is a measure of linearity between X and Y.

Let
y = bx + u
where y and x are demeaned random variables, u is a random variable, and b is a scalar. Then the causal effect of x on y is b, and
Cov(x, y) = bV(x) + Cov(x, u).
Suppose Cov(x, u) = bV(x). Then for any nonzero b, x causes y but x and y are uncorrelated.Let X and Y be normal. Oh, they are independent. Oh, your example doesn't work.

Corr(X,Y) is a measure of linearity between X and Y.
There are several correlation coefficients that do not require the assumption of linearity. You use the Pearson coefficient. That's fine. But in that case, you should still know that linearity is a convenient assumption (linearity), rather than something central to the definition of correlation.

Let X and Y be normal. Oh, they are independent. Oh, your example doesn't work.
My example does "work". I have no idea what your attempting to say.
The point of the discussion here is that linear correlation is a good measure of dependence only for specific random variables like normal random variables. Otherwise, you can have stochastic dependence without linear correlation.
A point made above is that it is easy to find examples where x causes y but the relationship is nonlinear in such a way that the *linear* correlation is zero. Such examples do show that causation need not lead to linear correlations, but they may be misleading in that one might conclude that causation from x to y implies some of sort of dependence between x and y. The example with a third, confounding variable shows that x and y can statistically independent, nor merely linearly uncorrelated, when x causes y.
None of this has anything to do with normality.