In reality, the compiler will turn the == operator into a ceq IL code, and the operator you mention will not be called.
The reason for the operator in the source code is likely so it can be called from languages other than C# that do not translate it into a CEQ call directly (or through reflection). The code within the operator will be compiled to a CEQ, so there is no infinite recursion.
In fact, if you call the operator via reflection, you can see that the operator is called (rather than a CEQ instruction), and obviously is not infinitely recursive (since the program terminates as expected):
double d1 = 1.1;
double d2 = 2.2;
MethodInfo mi = typeof(Double).GetMethod("op_Equality", BindingFlags.Static | BindingFlags.Public );
bool b = (bool)(mi.Invoke(null, new object[] {d1,d2}));
Resulting IL (compiled by LinqPad 4):
IL_0000: nop
IL_0001: ldc.r8 9A 99 99 99 99 99 F1 3F
IL_000A: stloc.0 // d1
IL_000B: ldc.r8 9A 99 99 99 99 99 01 40
IL_0014: stloc.1 // d2
IL_0015: ldtoken System.Double
IL_001A: call System.Type.GetTypeFromHandle
IL_001F: ldstr "op_Equality"
IL_0024: ldc.i4.s 18
IL_0026: call System.Type.GetMethod
IL_002B: stloc.2 // mi
IL_002C: ldloc.2 // mi
IL_002D: ldnull
IL_002E: ldc.i4.2
IL_002F: newarr System.Object
IL_0034: stloc.s 04 // CS$0$0000
IL_0036: ldloc.s 04 // CS$0$0000
IL_0038: ldc.i4.0
IL_0039: ldloc.0 // d1
IL_003A: box System.Double
IL_003F: stelem.ref
IL_0040: ldloc.s 04 // CS$0$0000
IL_0042: ldc.i4.1
IL_0043: ldloc.1 // d2
IL_0044: box System.Double
IL_0049: stelem.ref
IL_004A: ldloc.s 04 // CS$0$0000
IL_004C: callvirt System.Reflection.MethodBase.Invoke
IL_0051: unbox.any System.Boolean
IL_0056: stloc.3 // b
IL_0057: ret
Interestingly – the same operators do NOT exist (either in the reference source or via reflection) for integral types, only Single, Double, Decimal, String, and DateTime, which disproves my theory that they exist to be called from other languages. Obviously you can equate two integers in other languages without these operators, so we’re back to the question “why do they exist for double“?