Hi,
When you deactivate the plugin, the standard jQuery bundled with WordPress will be used. It could be that this version is not compatible with your banner. I would suggest clearing the website cache, if you have any caching plugins installed.
If you have any more issues, just let me know.
Your cookie banner appears to depend on jQuery, so you need to untick the “Disable jQuery Core” option. Ticking this option will completely disable jQuery on your site.
and there is no way to exclude only the banner with some function?
No, because the option disables jQuery completely, so it’s either off or on. I would suggest looking into a new banner that does not require jQuery.