Short answer: No, beer made with barley is not considered Jain.

Why:

• Jainism forbids intoxicants. The five main vows (non-violence, truth, non-stealing, celibacy, non-possessiveness) are accompanied by strict self-control, including avoidance of alcohol and any substance that intoxicates the mind.
• Alcohol dulls judgment, fosters harm to oneself and others, and disrupts spiritual progress, meditation, and mindfulness. For this reason, beverages like beer (and other fermented or distilled drinks) are avoided by practicing Jains.
• This applies across major Jain traditions (Digambar and Śwetambar); both regard intoxicants as unsuitable for a Jain lifestyle, regardless of the fermentation source (barley, sugar, grains, etc.).

In short: the barley in beer does not make it acceptable for a Jain; the key issue is intoxication and the resulting harm to spiritual discipline. If you’d like, I can share more on how Jain scriptures describe the prohibition of intoxicants and the aims of purity of conduct.