I'm about 85% sure that snagging in Texas is illegal no matter what fish. However, what if the fish is a non-game/invasive species? Please just give positive feedback

Illegal on game fish yes but I'm pretty sure it's not for carp, gar, drum. I would think if it's legal for bow fishing then snagging is no different! But just go fish. Why snag?

In my opinion, you and I will snag a fish,it's going to happen. If it's bad enough snag keep it. It's not ethical or legal to try to turn it in as a lake record. Unless you are bow fishing which I don't do anymore, I am CPR only, once in a while I may keep a few too eat, but that's me.

Here's what TPWD website has to say on it.

http://tpwd.texas.gov/regulations/outdoo...evices-for-fish

Pole and Line

A line with hook, attached to a pole (includes rod and reel)

May be used to take GAME AND NONGAME fish.
It is unlawful to take or attempt to take fish with one or more hooks attached to a line or artificial lure used in a manner to foul-hook a fish (snagging or jerking). A fish is foul-hooked when caught by a hook in an area other than the fish's mouth.

"used in a manner to foul-hook a fish" If you are not intentionally using them to foul-hook then I bet you could keep them and you can fight this in court I am sure.
I personally will keep a foul-hooked fish if I am fishing for food. A tournament is different and you should not keep it.

Intentional snagging is illegal in Texas

For me that leaves little in the way of ambiguity. I don't know when this was originally implemented, but do remember fishing for buffalo fish as a child with a rig that was totally made to "foul hook" (by the above definition) the fish. More than 40 years ago, fishing on a barge on Lake Wichita....

The simple terminal rig consisted of a sliding egg sinker then a swivel with a leader tied first to a #10 (really small) treble hook followed about four to six inches back by a much larger 5/0 or 6/0 treble hook at the very end. So, sliding sinker, swivel, small hook, big hook. Fished on a surf rod with heavy braid (the old timey kind, not what we use today).

Some gooey dough bait was placed around the small treble hook, and nothing on the big one at all. The rig casted out from the outside railing of the fishing barge 20 or 30 yards or so. Then the pole set down not quite tight line and wait.

The "bite" would be the line getting tight and twitching or going more slack. The guy fishing this rig then grabs the rod and heaves to as hard and fast as he can like setting the hook hard and fast.

Most of the time the fish would be hooked in the gill cover/gills, sometimes in the belly or side with the unbaited big hook on the end. Sometimes in the mouth with the little hook, sometimes broke off when one hook or the other hung up. But a lot of buffalo fish were caught and hauled off to eat that way.

By the above definition that rig would be illegal now, may well have been then.