Did you try to drop the collection the collection of profiling from the mongo database you are targeting?
db.system.profile.drop()
If that does not help, it might be a different collection that is causing the issue on your end
Unfortunately the airbyte logs are not helpful in identifying the culprit
There are 2 ways to figure it out:
The hard way:
To figure it out, if you your own custom mongo setup, you can try figure out the log output of mongo ( https://www.mongodb.com/docs/manual/reference/program/mongod/#std-option-mongod.--logpath ) and tail that log stream and filter out for $project call
tail -f /replace/with/your/path/to/mongo.log | grep '$project'
if you are using a SaaS like Atlas, you should download the full file and look into: https://www.mongodb.com/docs/atlas/mongodb-logs/
Ultimately you will be able to see error log and identify the culprit collection then figure out what can be done about it
The easy way:
Connect to mongodb with same credentials you are giving airbyte and run
db.runCommand( { listCollections: 1.0, authorizedCollections: true, filter: {type: 'collection'} } ).cursor.firstBatch
which is exactly the same call airbyte is doing airbytehq/airbyte/blob/436de264cbb9402cfb8d7b6b8d0cd996efc4f659/airbyte-integrations/connectors/source-mongodb-v2/src/main/java/io.airbyte.integrations.source.mongodb/MongoDbSource.java (can’t post link 
)
If you are seeing a bunch of system tables (has “system.” in the name), that points out to your problem, you need to set up a user with lower access rights to the target db, a “read” user or “dbOwner”