As I recall from school, all reproduction is asexual or sexual. But it gets complex because asexually reproducing bacterium are able to laterally transfer genetic material. And then there are viruses out there incorporating themselves into genomes. And so it appears to me that the very basis of reproduction has and-ifs and it just gets more sophisticated from there.

For example, environmental factors are able to affect genetic expression as you observe with reptiles.

However, if you take a planaria (flatworm) and mechanically split it in the proper manner, you can get two individuals.

And then we toss in hermaphrodism: plants don't stop and go ahead and fertilize themselves because their genetics provides for two sets of sexual organs. The angiosperms have been very successful at an evolutionary level as we are able to witness by so much green.

>Why do some animals have sex determination which is not genetically determined?

So your Q is about "environmental sex determination" and the mechanism is genetic. The organisms have the genetic ability to express all sexual phenotypes and the egg of a reptile makes a genetic decision to express a certain set of genes based on an environmental cue if hot or cold. It's just a game time decision.

https://en.m.wikipedia.org/wiki/Environmental_sex_determination