I feel respect is given until it is taken away, but maybe that's just my asian heritage. It's better to show more respect than less if the situation is unclear. I think appearing haught only happens if you think about it, much like being awkward in a social situation only really exist if you think about it too much. It's possible to be respectful without being contrived.
What kind of person opposes a mosque though? What kind of person opposes the construction of a church of any kind?