I think that the person here basically wants to say
because of the chime and announcement, I don't always do not think it is annoying.
My biggest problem though is that おかげで/おかげだ is used. I just learned in my textbook that this is used when CAUSE X has lead to POSITIVE RESULT Y. I get that the speaker, in case I understood this correctly, wants to conceal his/her negative opinion. But I feel very very unsure about this interpretation of mine ^^ Since I learned that おかげで/だ is used in positive contexts, I fear that it won't possible to use it inside a negative statement, unless irony is at play here. But I've no experience with irony in Japanese so far.
Here's my full translation: (Very literal)
Yes. It sure is. But I do not always not think that (="that" due to と思います) because annoying chime and announcement.
Yes. It sure is. But I do not always not think so (= "I sometimes don't think of it in its function as a safety measure" see the pretext) due to the annoying chime and announcements.
I couldn't find a way to integrate the THAT in "I think that...". It never works because the clause it relates to is a causal clause at the same time. At least if I understood おかげで/だ correctly.