Well all of their energy is being diverted to the flowers, so growth of root structure no doubt is suffering. I myself would remove as soon as possible. Letting leaf and root develop first will result in better and bigger stawberries in the long run. I sometimes let them go a bit as they are so small i worry about knicking the plant itself as soon as I can get the blades on flowers alone I remove them. usually before they even open.

I always pop off all the first blooms as it will strengthen the plants and prepare them for what is to come later in summer. Allowing them to fruit so early in the season will stunt the growth of the plants. This year I was thinking I might even pull flowers for a whole 4-6 weeks before letting any of them fruit, as I need to get a new stand well established.

Strawberry.org says you should remove flowers and runners until July 1st for new plants. Which means no fruit for June bearers, and a small crop for day neutral and ever bearing.

I planted some Pineberries this year, and also some Purple Wonders for fun. Well I have yet to plant, they came kind of early. We had freezing weather last night. It should end in a couple of days I will be planting Saturday. Talking them out slowly and getting them used to outside. They appear to be greenhouse plants. I probably would have just planted them if the weather was right, but it is not.
I'm expecting some white and yellow alpines and a white Virginia. I currently have a strawberry plot I will be using for other plants next year. I build 2 new ones (raised beds), One is ready for the new plants, and the other is not done yet. I hope to transfer between the plots as the plants decline. Keeping 3 plots is ideal, but I need the room.

Specifically, I'm asking if cutting the fruit/flowers off such young plants is okay. I am definitely not letting any fruit develop this season, but these plants, though growing quickly, are still very small (were just planted dormant less than 3 weeks ago), and cutting the fruit stems off will be cutting maybe 1/3 - 1/2 of the foliage on some of them. Does cutting on such young plants stunt their growth, should I let them get a little bigger before cutting off growth? The roots were 6 inches long when I planted them, and I feel confident they're growing as quickly as the foliage.

Take the flowers off now. Your plants will be fine -- better than fine.

"Does cutting on such young plants stunt their growth"

No, leaving them on is stunting their growth, maybe why they are so small?