Short answer: In normal day‑to‑day Jain household practice, most pickles are avoided or taken very rarely, and olives/sauerkraut are generally not suitable because of fermentation and vinegar. Details:

Core Jain principles involved

• Avoid unnecessary fermentation and foods with very high micro‑life (lots of living microorganisms).
• Be careful with strong preservatives like common vinegar and alcohol‑based brines.
• Keep food simple, fresh, and sattvik, especially during Chaturmas and Paryushan. ( jainknowledge.com)

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1. Pickles (āthāṇu / achar)

Depends on how they are made:

1. Traditional sun‑dried, oil‑salt pickles (no vinegar, no deliberate fermentation)

- Example: simple mango or lemon pickle dried in sun, preserved in oil/salt, no water once stored. - Many Jain households do use these in small quantity in normal days. - Still, they are: - Very strong in taste, increase attachment to rasa (taste). - Often stored long‑term → more chance of micro‑life. - So, from a sādhana point of view: better to minimize or avoid, and avoid completely during Paryushan, Chaturmas austerities, upvās, ayambil, etc. ( jainknowledge.com)

1. Vinegar‑based or factory pickles

- Usually have vinegar, sometimes fermentation, preservatives, unknown processing. - Vinegar and strong fermentation are generally discouraged for Jains because of very high micro‑organisms and, at times, alcohol origin. ( jainknowledge.com) - Safer to say: avoid.

Summary for pickles:

• Simple home‑style, non‑vinegar pickles → many Jains take a little, but spiritually better to reduce.
• Vinegar/fermented/commercial pickles → avoid.

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2. Olives

Olives almost always come in one of two forms:

1. Brined / lye‑cured olives in jars

- Soaked for a long time in brine, lye, vinegar, or similar. - Long curing = fermentative processes and high micro‑life. - Often also with vinegar or preservatives.

1. Marinated olives (with wine vinegar, etc.)

- May have wine vinegar, alcohol‑derived ingredients, flavor enhancers.

Because of:

• Fermentation / curing over a long time.
• Often vinegar / preservative use.
• Strong taste and non‑Indian, industrial processing (hard to verify ingredients),

for a careful Jain practice it is best to treat olives like other fermented/preserved foods and avoid them.

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3. Sauerkraut

Sauerkraut is explicitly a fermented food:

• Shredded cabbage + salt, left for days/weeks to develop sour taste through lactic‑acid bacteria.
• This is exactly the kind of live‑culture, high‑micro‑organism food that Jain teachings advise against, especially where we deliberately promote and then eat huge numbers of micro‑lives. ( jainknowledge.com)

So, sauerkraut is not appropriate for a Jain diet that tries to minimize himsā at the micro‑level.

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Everyday vs festival/vrat practice

• Normal days (gṛhastha Jains):

- Some may take a little simple pickle with care. - Olives and sauerkraut: best to avoid, as they are clearly fermented/preserved foods.

• Paryushan, Ayambil, Chaturmas austerities, upvās:

- General rule: no fermented / high‑micro‑life foods, no strong pickles, no vinegar. ( jainknowledge.com) - So all three – pickles, olives, sauerkraut – should be left completely during these periods.

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Practical guideline

If you want to stay safely within Jain maryādā:

• Allowed with caution (small quantity; avoid in vrats):

- Simple home‑made, non‑vinegar pickle, freshly made or properly sun‑dried and oil‑preserved.

• Best to avoid altogether:

- Any fermented or vinegar‑based pickle. - Olives (brined/fermented). - Sauerkraut (fully fermented).

For broader Jain food rules you can see a simple overview here: “What foods Jains should eat and what should be avoided”