This is almost impossible to answer without being there, but I'll try and give some guidance from my Point of View:
Is it ever acceptable?
Absolutely - we've all got to eat and, despite best efforts and 'official guidance', sometimes our days conspire against us. It's something I've certainly done, especially with last minute meetings. And some meetings certainly have a food culture - I used to have a 9 - 12am Friday morning meeting, and we'd always grab breakfast at around 10:00am.
I also don't think anybody would look twice if you bring a drink and some sharing food such as cookies or doughnuts etc.
Is it ever completely unacceptable
I'd suggest it's never acceptable if there are clients, customers or senior (in comparison to yourself) colleagues in the meeting.
Also, I hope it goes without saying - but it should never done with "anti-social" foods. I.e, smelly foods, messy foods, hand food (Excluding sandwiches)
How do I mitigate the risk?
Following the culture is always the first rule. If your boss brings food, then that's almost always a cue that it's fine. You state that you're the only one, so this in itself is a warning sign.
Ask others and excuse yourself. If this is truly a once ever [x] meetings thing (Where x is a reasonably high number), then I don't think it's unreasonable to expect a bit of understanding. Especially for a 1:00pm meeting.
It also depends on the formality of the meeting - an informal catch-up with colleagues on your team is a world away from a formal board meeting.
In summary, however, if you're the only one doing it and these meetings don't fall into your local definition of "lunch time", then I'd suggest you avoid doing so.