Yes, you can file.
You should request a Form W-2 if you were an employee of the religious organization. If that organization has a moral objection to paying FICA (Social Security and Medicare) taxes, they can submit the necessary paperwork to the IRS to be exempt from making those payments. However, that is NOT your concern.
If they fail to give you a W-2, you can file a Form 1040 with Schedules C and SE and claim the income (at most $3,000) as self-employment income. No income taxes will be due because of the low income amount, and the self-employment tax will be, at most, $460. However, you will NOT pay $460 because you will qualify for BOTH the Child Tax Credit and Earned Income Credit and in fact you should get a refund of some amount due to these credits.
If you need professional help with this, email me at
[email protected] with a phone number and I will call you to discuss your options in detail.