Even though we've been planting natives for a number of years, we still don't have a yard that's 100% native—and likely never will.
It's generally recommended that people aim for at least 75% native, and I'm pretty sure we're well beyond that percentage by now.
And any new plant we get is always a native, so we're always increasing our percentage of natives.
We have some non-native plants
Honey bee getting some nectar
Why do we still have non-native plants when we believe that natives are the most appropriate?
First, it's expensive to buy enough plants for an entire yard all at once (and we don't collect from the wild!), and it would be a lot of work to replace everything.
Second, some heirloom plants, such as sedum or hollyhocks, don't cause any problems and may even have some habitat benefits. We also have some hosta, though each year I compost some when I have shade-tolerant natives, such as ferns, available as replacements.
We're getting rid of these gradually
We're gradually getting rid of Japanese pachysandra. (We grow a native variety of pachysandra, too.)
As far as I can find out, unlike myrtle, it hasn't been listed as an invasive plant, but the sheer amount of it planted in home and institutional landscapes means that there's less room for other, more useful plants.
We've pretty much gotten rid of all but one patch of pachysandra (around the base of our sugar maple tree) though we've been reducing this patch each year. We had planted it there a couple of decades ago, and it was the only thing that would grow there.
Why do I say we've "pretty much" gotten rid of it? I'm still finding bits and pieces in a variety of places around the yard. Every year, I try to get rid of it, but each spring I see some still popping up, though I believe in declining amounts.
We also got rid of non-natives that are over-used in general and that don't have much habitat value for the space they take up. We put forsythia and lilacs in this category, and we got rid of those long ago.
We don't tolerate these
The non-natives we don't tolerate are the invasive ones because they're a problem in the world beyond my yard.
And although they're not offically invasive, we're gradually getting rid of non-native, non-invasives such as Kousa dogwood (Cornus kousa). This is "the plant I love to hate."
Although petty spurge (Euphorbia peplus) isn't one of the "official" non-native invasives that is of ecological importance, it is non-native and it does definitely invade my yard. It's the bane of my existence.
The "flowers" are shown in the top part of the larger plant, but when it's young it looks like the small plant at the bottom right.