"I find it incredibly tedious, hate that it murders itself with its own conservative pomposity"

This quote by Fiona Shaw is a criticism of the tediousness of something, likely a task or activity. She expresses her ridicule for it by saying it "murders itself with its own conservative pomposity". This implies that the task or activity is excessively conservative and pompous, and that this is what makes it so laborious. It is most likely that the job or activity is overly strict and stiff, which it is not open to any type of imagination or development. This makes it dull and uninteresting, and Fiona Shaw discovers it exceptionally tiresome. The quote is a criticism of the absence of flexibility and creativity in the job or activity, and how it is so bogged down by its own conservative nature that it ends up being laborious and unenjoyable.