Can't it also be "They do not eat meat?"
No, though it sounds tempting and in colloquial Czech it would pass. But at the same time, colloquial Czech rarely if ever uses neutral plural pronoun as ONA but says ONI.
Nevertheless, the proper verb for 3rd person plural is NEJEDÍ.
Maybe it was just me, but I had a hard time understanding the voice for this one. I was thinking jedí or mají for They are eating meat or They have meat.