my Chinese friends always refer to Mandarin as just Chinese and the only time we make distinctions is when we discuss either dialects or compare different Chinese languages. it's not my place to decide whether someone should be offended or not, but as someone who is also white like your friend, I can tell you with full confidence don't listen to them, listen to actual Chinese people, because it's up for them to decide what is offensive in regards to their own culture and language.

virtue signalling and getting offended on someone else's behalf when they didn't ask is the absolute worst (and I know that because as a Slav I had non-Slavic people tell me I should stop calling myself a Slav because apparently it's offensive to me and I'm playing into American stereotypes, when this is literally what us Slavic people do. I imagine POC have it twice as bad. don't do be like that, don't listen to people like that)