Is it safe to use my MacBook while it’s charging?

you got blamed wrongly.

That computer is a battery-CAPABLE device. It is not optimized as a battery-operated device. (It is NOT an iPhone.)

Your computer performs best when connected to AC power, such as the power adapter. It can use the full output of the Power Adapter AND when doing especially challenging work will also freely "borrow" power from the battery. In some cases, even with the power adapter connected, the charged state may decline during very stressful work.

When used only on battery, your computer has no extra cushion of power, and may perform more slowly. However, for ordinary non-stressful tasks this may not be objectionable (possibly not even noticeable.)

In general, you should ALWAYS connect a power source when it is possible to do so, and only run on batteries (which could be somewhat slower) when no power sources are at hand. Your Mac maintains its battery charge levels under program control, and will NEVER over-charge. 

You can plug in the computer whenever convenient to do so. Leaving the computer plugged in will not damage the computer or the battery. The MacOS manages the power/charging system very well. There is no need for you to micromanage the system.

Short answer: yes it is safe to use the computer while it is charging.

It is quite fine (actually recommended) to use on AC power when near an outlet, and use battery power when portability is required.