Is there a way to block or allow specific logs from being ingested?

You can use Exclude Rules or Include Rules to specify what kind of data is sent to Sumo Logic.

Exclude Rule: If you specifically exclude a message, it functions as a blacklist filter, and the data will never be sent to Sumo Logic. 

Include Rule: It does the opposite and act as a whitelist and will only allows you to ingest logs matching a specific regex filter.

More information about Include and Exclude rules can be found here