Some Jinjiang Inns are OK with foreigners, others aren't; you have to check the particular property you're looking at. If it's the Dongzhimen Embassy District one at No.23 Xin Yuan Xi Li Middle Street, then the Jinjiang website says 可接待外宾 "Can Accept Foreign Guests."

"Foreign guest" normally means anyone not checking in with a Chinese ID card, including Taiwan and HK visitors.

(I checked Jinjiang Inns, the cheaper range of the Jinjiang group; perhaps you're looking for a higher-end Jinjiang Hotel.)