In C# you do have to think about it all the time. Most types have both properties and methods and in many cases it's not obvious whether the author of that type had the same idea about whether or not something should be a property or a method as you do. Where you only have to remember a name in Java, you have to remember both a name and its syntactic category in C#. One more thing to keep in mind equals greater mental load.
In fact, the guidelines for choosing between one and the other include considerations that should be of no concern to the user of a public interface (https://msdn.microsoft.com/en-us/library/ms229054(v=vs.100)....). If any of these implementation details change, the logical conclusion would be to change the public interface from property syntax to method syntax or vice versa. That's what I call inconsistent.
If you're saying that the choice between getX() and x() in Java is also somewhat inconsistent then you are absolutely right. It's just not a problem on the same scale as in C#.
And if the implementation of a C# property changes in any of the ways that would make it a method, that probably deserves to be surfaced as a breaking change in the API. That's a feature, not a bug. eg, I would certainly want to know if the implementation of a property was changed from a field access to a network call.
And if you look at the guidelines I linked to, you'll see that the criteria that are supposed to tell us whether or not to use a property are much more subtle than making a network call vs accessing a field. Can you really justify a breaking change to a public interface because a type conversion is introduced in the implementation of property?
I think disguising a function call as a direct variable access is much more problematic than calling a function that may or may not do more than return the value of a variable.
That said, I do realize that reasonable people can absolutely disagree on this issue.
>>Can you really justify a breaking change to a public interface because a type conversion is introduced in the implementation of property?
I just quickly re-read that page, but I don't see what you're referring to here.
"The operation is a conversion, such as the Object.ToString method."
But this only pertains to the conversion of the object on which the property is defined. In other words, you should have methods like ToString or AsEnumerable, rather than properties like String or Enumerable, even though other rules would indicate property to be valid (idempotent, fast, no arguments). This rule is just an indication that properties represent conceptual attributes of an object; and the result of a conversion of an object to something else is not an attribute.
Semantically, the difference between properties and methods is the same as the difference between data and behavior. Are you saying that it's not a useful distinction to have?