While probably not what you want to hear, when one has a unique aversive objection to something that is a widespread social norm within an industry and cannot realistically be argued to be harmful, the best solution may be trying to mitigate the sensitivity, rather than to change other's behavior.
Of course what is considered a norm and what is offensive is contextual to a society. It would, for example, be quite possible to have a society where office workers did not typically use underarm deodorant, and the resulting natural odors were considered, well, natural. Someone in that context objecting to the odor of their co-workers would be counseled that the issue is with their sensitivity, not others behavior. In contrast, in most current office settings, it would be the person not wearing deodorant who would receive some behind closed doors counseling (one could then ask about the case of objection to a co-worker's use of excessive artificial scent... but that is another topic)
You are in a society (and especially in a startup, a subset of it) where eating during informal small group meetings is not in general viewed as improper. In contrast, many startups foster a type of mindset which would view this type of thing as drawing a team together.
That's not to say that all activities which draw a team together are necessarily unobjectionable - if you didn't want to go out drinking as an official company function (because of the alcohol) or playing lasertag (because of the simulated violence) or participate in a holiday party tied to a particular religion, those are kinds of situations where there's a general acknowledgement that what may be positive for some is not positive for all, and accomodation is more likely to be made - and in some cases or places, may be legally required.
Or to take a more extreme example, some teams might feel "drawn together" by the act of sharing off-color jokes. While that may be a long tradition in many industries and subsets of society, there's a growing recognition that it is improper, can be very unwelcoming and exclusionary, thus it is generally not permitted now.
But for the specific issue of talking while eating, it may be deeply objectionable to you, but you are going to have a hard time making an argument for harm, at least as the listener. Any accommodation offered is going to be purely at the discretion of others - hence varying by situation and likely to be often forgotten. If planning to continue in an industry segment where this is common, the only truly universal, lasting, and reliable solution is going to be working to overcome the aversion itself.
To be clear, "working to overcome the aversion" is not the same thing as pretending that the issue does not exist. The process of coping with averse feelings can be a complex one, and while it may be something that some can accomplish purely by exercise of will on their own, for others it may be a path best pursued with assistance. This will be different for each person.