Is it good practice to transform some variables and not others?
About the question whether to scale only a subset of features, I would tell you to do it over all the features (at least the continuous numeric ones) since the goal of data-scaling is to put these data on the same &quot;reference scale&quot; to be fairly compared.
Nevertheless, having mixed data types (continuous numerical, categorical...) for your classification problem looks more appropriate for scale-invariant algorithms like the ones based on decision trees. More precisely, you can have a look at XGBoost, where the author explains in this link that you do not actually have to re-scale your data.
Actually, in a recent real use case at my company, we tried re-scaling data VS not re-scaling it applying XGB, and we had better results with the second option.