To pull or not to pull?

Things I keep thinking are human introduced but they’re actually native

This is Acalypha and native. It volunteers abundantly in the shade under our red oak.
Parietaria. Native. Also volunteers.

To be added: Purslane, Mollugo, bedstraws, peppergrass, yellow oxalis, Euphorbia maculata, Euphorbia dentata (wild poinsettia), Melothris pendula, Cynanchum laeve (milkvine), little barley

Plants that are human introduced but not a big problem in undisturbed areas

Armeria serpyllifolia, thyme-leaved sandwort. Human introduced but not aggressive invader. This one was an accidental import from TX.
Seed leaves with one tiny true leaf
Several with seed leaves only
In our yard, we have both a human-introduced geranium and a native geranium. I’ve only seen these two species in our yard so far but there are several other species in Oklahoma. At the seedling stage they are identical, to the best of my knowledge. I wait until they bloom and seed to pull the somewhat aggressive human-introduced one. The native one can crowd plants in spring too (they both die back by the peak of summer) so I will pull either near less competitive plants or new plants I’m trying to get started.
Fatoua villosa, non native.
Maple that blows in from the neighbor’s yard. I am not sure of the species but there’s nothing locally native here in that genus (Acer).
This grass starts out very delicate and bright green in a clump. The roots are shallow and easy to pull. Abby told me what it was last year and i have tragically forgotten again but I remember it’s not native.

To be added: chickweeds, henbit, deadnettle, dandelions, shepherds purse, white clover, yellow clover, crepe myrtle, Sherardia arvensis

Human-introduced species that can disrupt the local ecosystem aggressively

Fish mint. Weird one! Leaves almost violet like before blooming and now I can see they are less round and have touches of red. Plus it smells strongly when crushed. After finding some possible epazote in the backyard, I wonder if a few owners back at this house were into growing a lot of culinary fun!
Invasive dayflower. I wrote up how to distinguish it from the native perennial in another post. I am not sure how invasive it is outside disturbed areas, but it does seem to crowd out and overgrown things like white avens in my yard, so we’ve been actively removing it.

To be added: privet, Bermudagrass, King Ranch bluestem (aka KR grass), salsify, some brome grasses, some Poa grasses, some Palsalpum grasses, crabgrass, autumn clematis, that one aggressive sedge

Native species but no thanks

Stickers/sandburs/goatheads are native but they hurt. They like sand. if we were managing a larger area of land, I would leave them alone outside our paths and main dog area, as I’m sure something needs them. I’m not keeping them in our small space though.

Bigger
Smaller
Cottonwoods blow in from everywhere. Do not need dozens of baby trees.

To be added: baby walnut trees, baby red oak trees, poison ivy

Native species that sometimes crowd my new stuff or have aggravating seeds

Four different sizes of Chenopodium seedlings. A common name for this genus is lambsquarters. I like to make sure there are some around, because it’s a hostplant for Hayhursts Scallopwing skipper, the seeds are food for birds, and the leaves are edible to humans as raw or cooked greens. But it seeds ABUNDANTLY and I don’t need all of them.

To be added: trumpet vine (as with the trees, I don’t have enough room), sticky seed pod legumes, bidens (sometimes) and white avens (sometimes)