Praise be to Allaah.
The general principle with regard to foods is that they are permissible, and nothing is disallowed except that for which there is evidence that it is haraam and should not be eaten.
But the problem is the use of yeast in these pickles.
It says in al-Mawsoo‘ah al-‘Arabiyyah, under the heading Khameerah (yeast):
Yeast is a substance that ferments the dough when making bread. Its effect is the formation of carbon dioxide which created bubbles that make the colour of the dough lighter, and makes the dough expand during baking and rise and increase in size. Yeast is also used to make beer, nabeedh and other alcoholic drinks. The he yeast that is used commercially is made from colonies of microscopic single-celled yeast organisms. Although there are more than 600 kinds of yeast, only a few of them are used commercially.
Based on that:
If the amount of yeast in these pickles and the like is very little, and it has dissolved in them, so that it does not have the effect of causing intoxication or languor, there is nothing wrong with using yeast in them, and eating these pickles.
But if the yeast has a lasting effect on them, such that if the one who ate a lot of these pickles would become intoxicated or tired, it is haraam to use the yeast in them, or to eat anything to which yeast has been added in this way.
Thus it become clear that pickles made from permitted foods are permissible. It should be noted that the vinegar which is put with these products or that is produced by pickling these materials, comes under the heading of drinks that are originally permissible, and is a type of food that the Prophet (blessings and peace of Allah be upon him) ate and praised, saying, “What a good condiment is vinegar.” [Narrated by Muslim, 2051].
For a more detailed discussion on the ruling on vinegar, please see the answer to questions no. 106196 and 113941.
There is also nothing wrong with eating bread made with yeast. The yeast (khameerah) that is added to the dough does not come under the heading of khamr (intoxicant) that is haraam, and does not have any effect of causing intoxication or languor, especially since cooking it with fire alters the yeast completely, so that it no longer has any effect.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) was asked:
How should we respond to the ruling on the yeast that they put in flour to help leaven it and make it easy to cook, as some people say that it is khamr and it is not permissible to use it?
My response to that is that there is nothing wrong with putting yeast in the dough for the purpose of leavening it, because this does not affect it at all. Moreover, I do not think that this yeast would cause intoxication if a person were to eat it. The basic principle concerning all foods and drinks and clothing is that they are permissible, unless it is proven that they are haraam, because Allah, may He be exalted, says (interpretation of the meaning):
“He it is Who created for you all that is on earth. Then He rose over (Istawa) towards the heaven and made them seven heavens and He is the All-Knower of everything”
So there is nothing wrong with putting yeast in the dough to leaven it.
Fataawa Noor ‘ala al-Darb (tape 70, side b)
And Allah knows best.