look, things aren't binary.. No, it's not "support", obviously they largely stand by their country over the US. But it's not North Korea; they understand that life is good in the US, propaganda aside. They don't think our systems don't work _in general_, they think it wouldn't work _for them_
to directly answer your question, if you think this is a war of ideology, this move doesn't do the US any favors, regardless of how necessary or justified it is
I'd say banning TikTok has a small downside. Sending citizen info to the opposing super power should be prevented (it's not binary like you said, but the risk is high, so the impact is potentially high). The downside is some Chinese will look at US as hypocritical.
Fine.
Here are 3 geopoltical issues that are way bigger than TikTok banning: Hong Kong, Taiwan, disputed islands on South China sea with Vietnam and Philippines. These issues evoke much stronger nationalism.
A large portion of Chineses probably already look at US as very bad guy regarding these 3 geopolitical issues already. Trying to turn Chinese's regular person to be positive by not banning TikTok is not worth it.
It's not like "oh yeah, I like US now because they don't ban tiktok, even though they try to help taiwan, hong kong, and etc. It's fine. TikTok is way more important here." Probably said no Chinese person ever.
I'd guess it's a very small percentage.