There was no context given in this article with reference to job-related, or even a non-meal meeting.
Pence told The Hill in 2002 that he “never eats alone with a woman other than his wife,”
Not saying I like Pence, but this cherry-picking of history, out of context just to find mud to sling is already beyond ridiculous.
Business meetings over a meal is a thing. Or even a more casual meal with coworkers, where you can talk shop. Or even get to know one better then float the cool or good projects their way. If he never eats alone with a man either, then it's ok, but in business inherently favoring one gender over the other is illegal. In some places, who gets assigned the projects or committees strongly determines your career trajectory.
Government meetings can be the same way. Getting a meal together, is sometimes part of significant negotiations. Say he has to meet with the leaders of the different parts of congress, and dinner time is the only time to do it. If he meets with McConnell and not Peloisi that is a sexist issue.
If his rule the "never" part is so inflexible that it does interfere in his job, it can be a thing. So to be "safe" he should never eat alone with anyone other than his wife. gender should be an issue, if eating is so special and sacred to him, he shouldn't do it with anyone other than his wife.
There is nothing inherently "sexy" about eating. it' sometimes necessary to eat with coworkers its not the same as going out on a date. I don't like to do it, but I have on occasion. Both in groups and one-on-one. Mostly I don't like to because of my allergy food restriction issues, so i don't want to come off really picky.