I'm looking for a plant that has white or blue flowers that will survive in full sun

I google searched Stratton WA...
so... near Perth?

On checking y'alls climate, it looks Mediterranean.
so... I'd be looking for drought tolerant plants...

maybe check the salvia family... some nice blue / white bloomers there...

I'd be hesitant to mention lantana... Apparently you have a huge problem there with that group of plants...

You know? lot of blues / whites among the bearded iris...
and... spiderwort do fine in the drought at my house with blue / white flowers...

How about passiflora?

We probably need some idea of the amount of space you have... the passiflora at my house is climbing trees and covering a large part of my yard... If it wasn't so important as a host plant for the butterflies... I'd start to get a bit concerned...

Full sun means different things in different places.
Where I live in Florida, almost NOTHING rated for Full Sun really means...full sun.Not all day sunrise to sunset full sun.
It means either 4 or so hours of morning full sun, or 4 or so hours of afternoon full sun, usually starting about 4pm. The hours between 12-4 are too much full sun for most ornamental plants.
Where as full sun somewhere like Oregon, or Washington, of a place that doesn't have temps of 90F from basically March to November, can do a different amount of full sun.
When we get plants labeled full sun at the nursery, that means dappled shade, or morning sun.