It is. It’s not something you’d be reprimanded in your civilian job for, and people wouldn’t say anything rude about it or anything, but it certainly lowers your social standing. Culturally speaking, it is sometimes considered to be a mark of poor virtue and decision-making skills, on a par with alcoholism or a gambling problem. It’s definitely a hot gossip item at the very least. That’s changing, but overall it’s considered a social ill, even among strongly progressive people.
The U.S. military certainly is “old fashioned”, although I think that’s putting it generously. In this particular detail, though, it’s not really far removed from the public thinking on the issue. It’s totally non-controversial, and it’s considered several hundred times more mundane than the military’s stance on homosexuality.
This is assuming that by “having” you mean “giving birth to”. If you just have a child from a previous marriage, that’s really no big deal, in or out of the military.
“Some societies” pretty clearly refers to the U.S., as it’s in a section about an American colloquialism. And it’s pretty accurate.