Short answer: It depends on the pachchakkhan (vow) you have taken for Paryushan and your sampradāy’s maryādā.

General guidance, kept simple:

• If your vow allows fruits: Dates (khajur/kharek) are generally permissible because they are a single-seed fruit. Eat them only in daylight, after careful inspection for insects, and without any processing (no glaze, oil, syrup, or additives).
• If you have taken stricter pachchakkhan: Avoid dates. This includes vows like only-boiled food (ukāḍu), no raw items, no sweets, or avoiding seed‑bearing fruits (bahu‑bījī/beeja-yukt items) by personal or temple code.
• Always avoid: anything fermented, cut or handled after sunset, or with signs of infestation.

Tradition-specific notes:

• Shvetāmbara Paryushan: Many avoid green vegetables during these days; fruits are usually allowed unless your guru/gaccha has directed otherwise. Dates then are typically acceptable if clean, unprocessed, and taken before sunset.
• Digambara Das-Lakshan: Many observe upavās/ekāsan/beāsan and often restrict to very simple or boiled food; in such stricter observances, raw fruits (including dates) may be set aside.

Best practice:

• Prefer plain, unprocessed dates; avoid glossy or syrup‑coated ones.
• Check thoroughly for insects or spoilage.
• Honour the specific maryādā of your guru, sangh, or family tradition; when in doubt, abstain.