Disable the toolbar module in install profile
From an install file perspective, you can use a combination of module_exists and module_disable, in an implementation of hook_enable.

Example:

function MYMODULE_enable() {
  if (module_exists('toolbar') {
    module_disable('toolbar');
  }
}


Module enabling/disabling isn't within the scope of a make file, so that won't work.

Lastly, as far as I'm aware, if a module is not declared as a dependency of a profile, the it won't be enabled.  If I'm mistaken, you can still use the code shown above to disable the module (although I can't 100% confirm where to put it, as I've never made an install profile).