Are records of a 501c3 organization public information?

Yes, the exempt application (Form 1023) including supporting documents and the annual income tax return (Form 990 of Form 990-EZ and supporting schedules) have to be made available for public inspection or you can provide copies for a nominal fee.

Even if not provided, the information can be obtained from the IRS.

The instruction to Form 1023 and Form 990 discuss what has to be available for inspection. You should review those so that information not required to be disclosed is not disclosed.

If you want to see public records Guidestar is a good place to start:

GuideStar nonprofit reports and Forms 990 for donors, grantmakers and businesses