I have seen atleast one paper claiming they have used DAPI to exclude dead one but some literature stated that DAPI does enter into live bacteria unlike other cells.
DAPI will also stain live cells. Check out a Live/Dead approach (e.g. BacLight). SYTO9 (or SYBR Green I, AO) dye will stain all cells (live and dead), while propidium iodide will stain only dead or damaged cells. Links to microbiome FACS viability staining papers below.