Would such a holy place accept a "monster" as yourself? The leading religion on this island isn't particularly fond of dragons.
Even monsters have hearts!
Plus you're disguised. Nobody will know you and very few will care who you are as long as you don't draw attention to yourself.
Plus it's a place of pacifism. I assume violence is forbidden, so the most they can do is escort you out.
...but then they could maul you when you step outside the threshold...