HaLeivi, what is this “on top”, “in parallel”. If someone uses “secular knowledge” to steal, to waste time, to offend people – then this is against Torah. If someone uses it to earn a living, to understand how Hashem’s world works, how to make life better for people – it is at basic level does not contradict Torah. (I am excluding cases like hiding Sefer Refuah because people did not deserve it).
Gemorah is full of not just medical but technical information about animals, farming, anything else in life. No Amorah would sow in the wrong season expecting Hashem to fix it. So, why would you do anything in our time without having all required knowledge.
Again, at the times of haskala things were different. Going to a university meant abandoning Torah.. It is not so in our days.