It depends. In my experience: in an academic laboratory I have been able to use common sense.

For example, gloves go on when working with strong acids/bases. The statement:

gloves apparently only give researchers a false sense of security that can dull the sense of touch and prevent you from recognizing chemical exposure

Does not apply as much when you are working with such corrosive agents, because you really should never be in a position where spilling 4 M HCl into your hands would go unnoticed.

When working with large quantitites of oils, even if non-hazardous, gloves go on and they will probably get oil in them.

When working with cell cultures, the goal is often to not contaminate the cultures. Some people prefer to wash their hands thoroughly and not use gloves, and they have been working at it for many years and they seem to do just fine. It’s a risk mitigation strategy - if the cultures have antibiotics and fungicides, risk is already not too high.

In an industry setting it is different. Companies often comply with specific standards and health and safety regulations. While the individual can use common sense, the people in charge of ascertaining compliance (sometimes ‘EHS’, Environment, health and safety personnel) aren’t necessarily chemists themselves, nor should they need to be aware of the identity of the transparent liquid in the flask that you are holding. So, generic rules are often set in place not only because of their practical utility but also to simplify enforcement. In some cases external auditors can come in (announced or not) and verify compliance - this, again is much simpler when the rule is ‘lab coat behind yellow line, gloves always on when touching a container with a liquid’ than having to interview each person to understand what they were touching without gloves and to understand their philosophy of why they chose to do so.