3DPrinting

The problem has multiple facets. Geometry is only one.

1. Cleanable geometry. Already discussed.
2. Additives in the plastic. Many plastics won't have been made around food safe equipment or may even have bad additives. Most 3D printing plastic isn't pure because most pure plastics don't print 'that' well (well, not as easily). They aren't expecting anyone to eat the plastic, so most make zero effort to keep unsafe (to eat) additives.
3. Temperature. Many of the easily printable plastics soften to the point of wilting below 100C. Sure, it won't crop up often, but put a large thin thing like a bowl in there, and I'd be surprised if it came out of a drying cycle unwarped.
4. Plastic around food. Most printed plastic is much softer than plastic utensils (not necessarily the "disposable" sort) at the store. There WILL be microplastics in your food with printed goods. (hell, depending on the task, plastic isn't a good idea even in many of the products at the store!) Plastic may be non-toxic, but so is asbestos. Asbestos is not chemically dangerous, yet it was outright banned, and doctors do not have a good idea what the presence of microplastics does.

can I 3d print PETG objects, use them, put them in the dishwasher, and then safely reuse them?

No.

The glass transition temperature (the temperature where plastic starts to become malleable) of PETG is 85°C, so if you put a PETG spoon in boiling water, it would deform and become pretty useless. However, if you used a high temperature plastic with a glass transition point above 100°C, you might be able to get away with this method.

Also, just to clarify, a dishwasher does not get to 100°C. You could use it to get the initial food off, but you would then need to boil the utensils manually on a stove to actually sterilize them.

There is no such thing as food safe plastic

Nonoilen filament printing is what you're looking for.

It's a pain to print with and I suggest you just don't print food safe objects.

Now I want to print molds and make carbon fibre cutlery just for shits and giggles.

You could investigate PVB which can be smoothed. It does soften at a low temperature though so you can't cook it or wash it in the dish washer. If it's well smoothed you can wash it with warm water and soap though.