If a certain set of genes predispose one to transgenderism, but require environmental factors (and no, not just coddling by parents), then it is still a genetic condition. They are hardwired in a way that allows the environment to influence them (whether through amplification, suppression, etc. of genes). Many diseases we consider "genetic" do not have complete concordance across identical twins. Genetics is very complicated & not nearly as simple as, you have this gene so you have this condition (though sometimes it is). It is a misnomer to assume only environment affects genetics; genetics affects the environment too!

It's interesting that you (likely) believe transgenderism is a mental illness, but you deny the genetic component of the disease. The same argument can be made for schizophrenia. Genes predispose individuals to develop schizophrenia; they are activated by immeasurable environmental factors. Twins will not always both develop schizophrenia, but there should be a fair bit of concordance between them at the population level.