Banks are in the service industry (as is just about everything else; only resource extraction and manufacturing are excluded), so not just "more of". It is definitively a service industry position.
> like being a cashier.
The physical action of the work is a lot like being a cashier, but the environment in which the work is done is usually different, and that environment (especially with respect to the type of clothing the people usually wear within that environment) is what traditionally defines "white collar". As such, tellers are considered white collar by most people.
Office environment is key to what you say. That is why you would be considered white collar. The literal white collars may be gone, but what you call "dressing like slobs" is just a modern adaptation of the same white collar idea.
Now, as it pertains to tellers, banks are typically considered to be an office environment, thus why most consider them to be white collar.
You've claimed this twice, but I would guess that almost no one thinks a bank teller is white collar.
Sure they work in an office environment, but their role is more similar to the cleaning crew than to the branch manager.
Nothing about the day-to-day work in terms of autonomy, education, responsibility or any other key intangibles of the job match "white collar". It's akin to being a secretary or a mailman or working in a call center.
And you confirm that they work in an office environment, so that bit isn't in question. Perhaps you are confusing most with all? It is certain that not everyone sees "white collar" that way, but we're not talking about everyone.