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Hi, in general it is compatible with those two tools.
But actually it doesn’t block anything automatically. You have to set up the rules by yourself and configure it by yourself.
For this blocking feature you need the premium version.
If you do not have the premium version the banner just sets the cookies with the users choice. What to do with that choice needs to be implemented by you.
See here some more documentation:
https://beautiful-cookie-banner.com/documentation/