Is C# Decimal Rounding Inconsistent?

From MSDN:

If there is a single non-zero digit in d to the right of the decimals decimal position and its value is 5, the digit in the decimals position is rounded up if it is odd, or left unchanged if it is even. If d has fewer fractional digits than decimals, dis returned unchanged.

In your first case

decimal a = 0.387518769125m;
Console.WriteLine(Math.Round(a, 11));

there is a single digit to the right of the 11th place, and that number is 5. Therefore, since position 11 is even, it is left unchanged. Thus, you get

0.38751876912

In your second case

decimal b = 0.3875187691250002636113061835m;
Console.WriteLine(Math.Round(b, 11));

there is not a single digit to the right of the 11th place. Therefore, this is straight up grade-school rounding; you round up if the next digit is greater than 4, otherwise you round down. Since the digit to the right of the 11th place is more than 4 (it’s a 5), we round up so you see

0.38751876913

Why am I seeing inconsistent results?

You’re not. The results are completely consistent with the documentation.