Forum new guy, but long time safety and health guy here. Typically the best bet to provide respiratory protection for a bearded person is going to involve a positive pressure hood system as others have mentioned. This could be a supplied air system via a hose, or a belt mounted PAPR system. The belt style PAPR is likely the simplest and safest set up for a non-professional.
Any type of negative pressure face mask style respirator (paper mask, half face, full face) is not going to work properly with facial hair. The term negative pressure is key here. These face masks all work because our inhalation creates a negative pressure inside the sealed face mask. This negative pressure forces (***** in) air in through the cartridges. Facial hair is going to interfere with the seal. This will result in not enough air going through the cartridges and/or unfiltered air coming straight in via the broken seal.
The hood/helmet systems work for two reasons. First is they don't seal around the face. They typically loosely seal around the neck or don't seal at all. Second is that these systems constantly supply positive pressure to the breathing area. So even if there is a bad seal it is less of an issue because air is always being forced out and away from the user's breathing area.
The biggest issue with beard friendly systems is cost. You are going to spend $500 to $1500 for a proper PAPR or Abrasive Blasting setup. Please go this route and get appropriate training if you are going to be doing serious work with serious exposure to hazards such asbestos, silica, welding fumes, high concentrations of solvents such as when painting a car or other hazards. These are the types of set ups that commercial car painters tend to use.
All of that said, I have a full beard and have used paper dusk masks (n95), half face and full face respirators. I do this with the realization that the effectiveness is greatly reduced. I only do so in situations where I could probably go without any respirator. Even if the protection factor is reduced 80%, at least some of the bad stuff is being filtered out. However, I would not suggest this if working with solvent hazards such as painting cars in a poorly vented garage. Or mold remediation. Or welding stainless. Or asbestos. Or any real hazards.
I cannot post links, but if you google "assigned protection factors" you will find info a handy OSHA or NIOSH resource on the types of respirators and how much they protect you.
Also, in regards to that Resp-O-Rator thing. Please don't use that for anything but nuisance dust. It likely has basically the same use case as a paper dusk mask. It would not be appropriate for solvents, welding fumes, or basically anything but annoying wood dust.
