I'm not sure why people have a problem with palm trees being planted. While SE/coastal areas of the metro feature the most optimal growing climate (and with the largest varieties of species), everywhere in the Houston has a climate warm enough to support the planting of many types of palms.
There are two native palm varieties specifically to the Houston area (sabal minor and sabal brazoria), but even if there weren't, it doesn't matter, since many palms have been shown to do well in Houston's climate, from dates to washingtonias to sabals. No palm is native to coastal California, doesn't stop places like LA from planting loads of them.
It really doesn't matter if a plant is native or not; if it can grow well, then there is no problem using it. Crape myrtles aren't native to the US, yet they grow just fine in Houston, and no one throws a fit at their presence.