Yes, a Jain can help a poor beggar of any religion, if the intention is compassion and relief of suffering.

From Jain dharma:

• Daya (compassion) is important.
• Helping the needy is शुभ when done without ego, attachment, or हिंसा.
• A Jain should try to give in a way that reduces harm.

So:

• Giving food to a hungry person is generally more proper than giving money.
• Giving money may be okay, but it is better to give it carefully, because it may be used for harmful things.
• If possible, give clean food, grains, clothes, medicine, or direct help.

If the beggar is unknown religion, that does not stop a Jain from helping. In Jainism, compassion is not limited by religion. The main concern is that the help should support non-violence and right conduct.

In short: Yes, help is allowed and good — but direct, harmless help is श्रेष्ठ.