Created a staging site for you, adding details below.

Which plugins create the conflict?
As I said – this is directly an issue of your theme with the WP Rocket cache because when the user is logged in – these bugs don’t happen (no cache for logged-in users, yet).
So again – it’s about which file to exclude caching or delayed execution.

Your theme should work with caching plugins, especially a popular one like WP Rocket, so please advise.