Typically, the job restriction that you see like on the Eureka items you mentioned (Nagi Anemos) is only applied to equipment that is part of "job identity gear", like the AF sets (the gear you get when you hit max level in ARR/SB/SHB, and the first weekly tome set in HW) and relics (which the eureka weapons are part of, as well as the anemos armor which is job identity gear since it's just the SB AF set but dyeable, while the hydatos armor sets aren't job identity so classes can wear those too).

Everything else that I can think of is equippable by the associated class.