I have a dataset with numerical and categorical data. The data includes outliner, which are essential for interpretation later. I’ve binary encoded the categorical data and used the RobustScaler on the numerical data.
The categorical binary encoded data does not get scaled. Is this combination possible or is there a logical error?
There's no reason why you couldn't do that, but there's also no point.
The reason why you scale input features to be on roughly the same scale is that lots of inference methods get tripped up by features which are on vastly different scales. See Why does feature scaling improve the convergence speed for gradient descent? for more.
A binary feature which ranges from 0 to 1 and a continuous feature where the 25-75% percentile range from -1 to 1 are already on approximately the same scale.
Since a binary feature is easier to interpret than a scaled binary feature, I would just leave it and not apply another scaling method.