Please,check first post again.
I found temporary fix.
In CCleaner under System I unchecked Temporary Files and Web Shield is working with Pale Moon,Opera Presto and Opera Dev. again.
With this version of Avast a new file important for Web Shield is introduced and when it is deleted by CCleaner or probably other cleaners,
it is not recreated until reboot.
Don’t know why Firefox and IE11 are not affected.
I don’t use Chrome,but it looks like it is also not affected.
Developers,please fix this.