Well, why did the LL want to inspect after the LA and only seem to mention the poster?
When our tenant neighbours have caused problems in the past, we have approached the LL and he has gone round and (for example) told tenants to bring their bins in , timely, and clear up spills.
If no other activity occurred, the poster may not even have been noticed. But it does sound like there are activities associated with this interest.
Anyway, as others have said, conservation areas have extra requirements, leasehold flats have extra requirements and so we have to accept we have to live like social creatures.
If I was asked to remove an offending or unnecessary declaration of an activity or interest I would certainly try and comply.
I am all for freedom of speech and democracy but if the house is not for your use as a business/billboard, then hire somewhere that is.
Sometimes we just want to switch off from the vagaries of politics and seeing a political poster whilst I'm out walking my dog, or going into my house next door, day in, day out, is just not desirable!
Do us all a favour and take it down, please.