To solve this problem, we need to analyze each of the given statements and determine which ones are true. We will use the properties of the greatest common divisor (GCD) and the least common multiple (LCM) to do so.

1. **Statement (1): The product $MD$ cannot be less than $abc$**

By definition, for any integers $a, b, c$:
$$\text{GCD}(a, b, c) \cdot \text{LCM}(a, b, c) = a \cdot b \cdot c$$
This is a fundamental property of GCD and LCM. Therefore, the product $MD$ (where $M$ is the LCM and $D$ is the GCD) is exactly equal to $abc$. Hence, it cannot be less than $abc$.

2. **Statement (2): The product $MD$ cannot be greater than $abc$**

From the same property mentioned above:
$$\text{GCD}(a, b, c) \cdot \text{LCM}(a, b, c) = a \cdot b \cdot c$$
This implies that $MD = abc$. Therefore, the product $MD$ cannot be greater than $abc$.

3. **Statement (3): $MD$ equals $abc$ if and only if $a, b, c$ are each prime**

This statement is incorrect. The equality $MD = abc$ holds for any positive integers $a, b, c$, not just when they are prime. The property of GCD and LCM does not require $a, b, c$ to be prime.

4. **Statement (4): $MD$ equals $abc$ if and only if $a, b, c$ are each relatively prime in pairs**

This statement is also incorrect. The equality $MD = abc$ holds regardless of whether $a, b, c$ are relatively prime in pairs. The property of GCD and LCM is always true for any positive integers $a, b, c$.

Based on the analysis, the true statements are:

1. The product $MD$ cannot be less than $abc$.
2. The product $MD$ cannot be greater than $abc$.

The final answer is $\boxed{\textbf{(A)}\ 1,2}$