The correct answer is $\boxed{\text{A}}$.
A vector space is a set of vectors that can be added together and multiplied by scalars. The dimension of a vector space is the number of vectors that are linearly independent.
Two vectors are linearly independent if they cannot be written as a linear combination of each other.
Orthogonal vectors are vectors that are perpendicular to each other.
The vectors $X_1, X_2, … X_M$ are non-zero, orthogonal vectors. This means that they are all linearly independent and they are all perpendicular to each other.
The vectors $-X_1, -X_2, … -X_M$ are also non-zero, orthogonal vectors. This means that they are all linearly independent and they are all perpendicular to the vectors $X_1, X_2, … X_M$.
The vector space spanned by the 2M vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$ is the set of all vectors that can be written as a linear combination of the vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$.
The vectors $X_1, X_2, … X_M$ are linearly independent, so they can be used to span a vector space of dimension $M$.
The vectors $-X_1, -X_2, … -X_M$ are also linearly independent, so they can be used to span a vector space of dimension $M$.
The vector space spanned by the 2M vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$ is the union of the vector space spanned by the vectors $X_1, X_2, … X_M$ and the vector space spanned by the vectors $-X_1, -X_2, … -X_M$.
The union of two vector spaces of dimension $M$ is a vector space of dimension $M+M=2M$.
Therefore, the dimension of the vector space spanned by the 2M vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$ is $\boxed{2M}$.
Option B is incorrect because the dimension of the vector space spanned by the 2M vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$ is not $M+1$. The dimension of the vector space spanned by the 2M vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$ is $2M$.
Option C is incorrect because the dimension of the vector space spanned by the 2M vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$ is not $M$. The dimension of the vector space spanned by the 2M vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$ is $2M$.
Option D is incorrect because the dimension of the vector space spanned by the 2M vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$ is not dependent on the choice of $X_1, X_2, … X_M$. The dimension of the vector space spanned by the 2M vectors $X_1, X_2, … X_M, -X_1, -X_2, … -X_M$ is always $2M$.