You mentioned natives (the virginia creeper and oleander, texas sage) and so did I.
Those aren't natives (creeper, oleander and sage). They just do well in this climate.
Well "need constant care" is the flip side of non-native...
Actual I was being too general here. All of the vines I named need constant care but the shrubs I named just need periodic watering and they're definitely not invasive.
For privacy hedge, native evergreen shrubs (again I was searching New Mexico) include
coyotebrush, desert ceanothus, mountain mahogany, choisya (mexican orange), shrubby cinquefoil, common juniper, evergreen sumac, red barberry, agarita. All should be easy care, low maintenance, and have good habitat value, full sun and drought tolerant.
The plants you named are nice but this person is asking recommendations for a privacy screen. The only plant you mentioned that is somewhat suitable for this as far as growth rate, size and density is the coyote bush and that plant is deciduous (obviously not ideal for privacy).
I'm not trying to be disagreeable but I know a lot about landscaping in this climate. Though they're not native, an oleander or euonymus japonicus hedge makes an ideal privacy screen and believe me they are sustainable.