I believe it is allowed to cross this border with any nationality, assuming you have the proper visa or can enter the country without a visa.
You can find examples of various non-locals crossing the border, such as Barry's Border Points and TripAdvisor poster "panik_uk", both of whom report no trouble crossing with a UK passport. You can also see an "all passports" sign at the Bulgarian border post on Google Street View. Furthermore, eKapija reports that in 2017 this border crossing was upgraded to handle cargo traffic, which doesn't directly answer your question, but suggests that this is a "full" customs point which should generally have no trouble with any normal sort of crossing.
While anything in the world of immigration and customs is subject to change at any time, it seems this crossing point, like almost all crossing points in Europe, has been open to all nationalities in the recent past, and I would not expect this to change without plenty of notice.