Well, Sunny Toast Airport had a Notam saying it was closed due to extreme weather
In whose opinion? The PIC is the sole judge of whether it is safe to land or not some tool in the safety car. In Eurpoe they can 'close' airports due weather but here it is the PIC's call.
You do the approach if you can get visual you land. If you don't you go around. Simple as that.
If the whole joint is underwater it needs to be NOTAM'd closed due flooding but to say the place is closed just because it's raining hard is ridiculous.