You can bypass the IDE's preprocessing by placing all your code in .cpp and .h files, instead of .ino or .pde. You still need to have at least 1 .ino or .pde file which has the same name as the directory it's in. But that file can be empty.
The Arduino IDE supports .cpp, .c, and .h files within your sketch. They are NOT preprocessed in any way. If you want to use the normal Arduino functions, you must add the #include <Arduino.h> line in each .cpp file.
Within those .cpp files, you can define classes and use templates. You can also use them in .ino files, but there's a pretty good chance the IDE's not-too-smart preprocessing step will attempt to extract global-scope function prototypes. But that preprocessing stuff is NEVER used on .cpp files.
Likewise, the .cpp files are NOT parsed for includes to infer which libraries to link into your code. So in that empty .ino file, you can place #include <Library.h> lines, merely as directives to the IDE's build system to tell it which libraries to link. Then you can include only the library headers needed in specific .cpp files which call those library classes.... so your other .cpp files remain free of namespace clutter.
Very few people seem to know this feature exists, but indeed the Arduino IDE does support real C++ compilation without troublesome preprocessing. You merely need to add the .cpp files to the directory, and then do your coding in those .cpp files instead of .ino files.
Of course, there are a couple C++ things you don't get, not because of the IDE, but due to limitations in the underlying AVR toolchain. The avr-gcc compiler does not support exceptions, and avr-libc does not provide the C++ stdlib classes & functions.
But you can bypass the preprocessing step. It's as easy as just creating .cpp files in the sketch directory!