It could be you are remembering something by a different author.
Associating "Alphans" with eating synthetic foods reminds me not of Asimov, but of Marion Zimmer Bradley. Cholayna in City of Sorcery was from Alpha, and did not eat animal products (at least, not meat products), but primarily synthetic foods. During the mountain trek the women made, she had to eat meat products as other options were not available. Sounds very much like your description, but the wrong author. (Note that she did not eat only synthetics; the issue was animal foods.)
Perhaps this will ring a bell: she forced herself to eat travel rations which were a kind of dried meat bar. When they were somewhere with proper cooked food, she tried, but could not bring herself to eat it. As I remember it, she shuddered, and said that it was one thing in a bar, but when it still looks like a leg or a wing....
Here are some quotes from the book, relating to Cholayna and meat. Perhaps the quotes or scenes, and/or character and location names, will ring a bell:
Camilla, on the way to their last meal in Thendara before hitting the trail:
It doesn’t meet your criteria for edibility, Cholayna, I know you try
not to eat anything that ever moved of its own accord, but you’ll have
to get used to that on the road, anyhow.
At Barrensclae, when Jaelle hunted, skinned, and cooked a chervine calf and Cholayna shudders, eyes averted, Magda thinks:
This assault on her ethical principles—Magda knew Cholayna had never
eaten meat, or anything which had once lived, before this—must be the
final trial. But she had kept silent about it, which could not have
The scene I mentioned above -- in the robber village, having the drugged meal:
Cholayna said faintly, “It looks—still looks too much like the—the
living animal. I’m sorry, I—I tried. When it’s just a—a bar, or a
slice, I can manage it, but—but this is a wing!
In camp, on the way from the Kadarin to Nevarsin:
Listen to me, both of you,” Cholayna interrupted. “Settle your places
in the pecking order somewhere else, and don’t use me as your excuse!
I am trying to eat as much as I can of your damned filthy food, but
it’s not easy for me, and I don’t need reminding all the time! I will
do the best I can; leave it at that, will you?"