We need a language to read a book, and that affects our thought process, as we start thinking like the author and behave in a manner we perceive from the books. Like how someone speaks under the influence of alcohol, books n authors too influence.
Sawdust that is created from cutting natural wood is safe for your compost no matter what kind of tree the wood comes from. Just make sure the wood has not been treated with any chemicals. Another option with sawdust is to try mixing it in with potting soil.
It can rob the beds of nitrogen while breaking down, and it can shift the soil's ph too much. Once the sawdust has rotted well between the beds, I have worked it in with compost for the next years growing.. Good compost tends to help the beds stay in a good zone ph-wise.