If you use a solid vinyl panel (you can get vinyl fence panels) between the rails and stiles, you probably could make a reasonably sturdy gate without diagonal bracing. But such a gate may not provide the desired effect.
If you do not want a solid gate, you may be able to use vinyl lattice as a panel. Vinyl lattice is a one-piece molding so there won't be any movement between the "slats". In effect this would be a whole bunch of cross braces.
The "Senior Member" designation under my name doesn't mean I know a lot, it just means I talk a lot.I've been a DIYer since I was 12 (thanks, Dad!). I have read several books on various home improvement topics. I do not have any current code books I can refer to. I was an apprentice plumber for two years.