Yes, the phrase can be used in the context of a platonic friendship, although I believe you’ll find it most often used in the context of a date. That said, here is one example where the context seems to be outside of a romantic relationship:
After having missed several lunch appointments with a friend, the student made plans to meet a friend for lunch. At 5 o’clock the student realized: "I stood up my friend again".
Source: The Self-Conscious Emotions: Theory and Research, 2013
It looks like Oxford focuses on the most common use of the term in its definition, while Cambridge defines the phrasal verb more broadly. I wouldn’t call either definition wrong; I’d just say that Oxford’s might be incomplete.