You do need Fc receptor blocking if the cells you are analyzing express Fc receptors.
If you do not need to use costly reagents then you can also do Fc receptor blocking by using sera from the host organism, such as if you are using mouse samples then mouse sera can be used for receptor blocking- as the sera will have IgG that will occupy the Fc receptors.
I would stain cells in FACS buffer (1% BSA) with chosen antibodies on ice for 30 minutes. I did not incorporate any other specific blocking steps prior.
It's worth noting that, as phagocytes, monocytes/ macrophages will internalize Phenol red in you growth media. Upon interaction with intra-cellular enzymes, this will create 'auto-fluorescence'. As a result, you should look to culture your cells in Phenol red-free media.