Do people with mild dementia get food cravings?

My late husband who never liked seafood developed cravings for fish in the last 6 months of his life. And that is all he would tell me that he wanted for supper.
It was kind of comical as I remember many years earlier when we had gone to Red Lobster(as I have always loved seafood)my husband ordered the only chicken dish they had on the menu at that time.
And like your husband once he had something in his mind that is all he would talk about and drive me kind of crazy.
Humor him when you can and don't worry about when you can't. He'll be ok.

https://www.alzheimers.net/11-3-14-dementia-food-cravings

It's quite common to get food cravings for elders with dementia and Alzheimer's, yes. Above is a link to an article on the subject.

Better to have cravings and desire some kind of food than refuse to eat pretty much anything, even foods that in the past were favorites.

My husband ate many sweet carbs prior to being diagnosed with dementia. A blueberry muffin for breakfast, ice cream twice a day, as well as cookies and Tastyklairs throughout the week. Now, he doesn't like sweets at all, just an occasional half a sticky bun or doughnut. What he craves are the tastes of his childhood (but only his paternal Italian side, not his maternal WV homestyle cooking side). As long as he eats, I'm not going to fuss about it. Better to live in peace as much as possible and not trigger him.

If he has "mild" dementia make his asking for a particular food part of a "task" he can do.
Get a whiteboard and he can write down the items he wants.
When you go shopping you can ask him what one or two items he would like.
When you get to the store he can try looking for the items.
My Husband would always pick up bananas and put them in the cart. Didn't matter if we had bananas at home so when he wasn't looking I would replace the yellow ones he put in the cart with the greenest ones I cold find.
Since you are far from stores just remind him that shopping is done on Wednesday. You can circle or highlight Wednesday on the calendar so it reminds him.
**If he is beyond writing items on a whiteboard or trying to locate an item in the store there are other ways that you can get him to "wait" for shopping day.
By the way if the food cravings are for odd foods or ones he did not like before you might want to mention it to his doctor SOME cravings are indicators of deficiencies in the diet and they may want to check levels for vitamins and minerals.

Doesn't everyone get food cravings?
I sure do.
That doesn't mean when I have a taste for Trader Joe Old Fashioned Potato Chips that everyone runs out and gets them.

We all get food cravings. Someone with dementia is no different. But in the immortal words of Mick “you can’t always get what you want”

Just because he wants a particular food, doesn’t mean that you have to provide it or that he will suffer if he doesn’t get it. There are many many dementia ‘cravings’ that don’t have to be provided – like calling the police because the neighbors are tunneling under the house to plant dynamite.

Curious, is he watching alot of commercials, when I see Milky Way add, I can't stop craving it. Maybe adds are putting things in his head.
At a certain stage in someone's life I feel like they should be able to eat whatever they enjoy eating, it's pretty much all they have left.
But please don't feel the need to up out ASAP and get it for him. Just jot it down and before your next shopping trip ask him if he still wants this or that. Then get it for him, because the craving may have passed

Yes usually Its sugar . My Mom Only ate Mostly Yoghurt. My brother stopped eating for awhile and then got back his appetite .