If there is a correlation for homosexuality, and transgender is a possible outcome of homosexuality, then there is also a valid correlation with transgender.
Yes, but if the effect re transgender disappears after controlling for homosexuality then the result isn't valid for transgender. It's like finding a correlation between people wearing shorts and people eating ice cream. Sure, the correlation is there, but it's not like wearing shorts causes someone to eat ice cream or vice versa, it's just that both wearing shorts and eating ice cream are correlated with it being a hot day.
Also, you have to bear in mind that the flaw in the MRI studies was not that they were measuring homosexuality rather than transgender. It was that they were measuring patterns of sexual arousal and using the results to define a male brain vs a female brain. (And then correlating to transgenderism.)
There was one such study with that flaw, but that's not the flaw I'm talking about. The flaw I'm talking about is taking a group of male transgender homosexuals and comparing them with a group of male cisgender heterosexuals, and then ascribing the difference to transgender whereas the difference could be explained by sexual orientation. Basically the flaw is using an improper control group that differs on more than the variable being investigated.
It's a completely different thing from the twin study correlations.
True, but that doesn't mean the issue of homosexuality as a confounding factor isn't present there either. Suppose we have a group of 100 transgenders with twins. We find an 80% concordance for their twins. Now suppose we control for homosexuality, that 80 of them are homosexual and 20 are heterosexual. All 80 homosexual ones are concordant with their twins and all 20 heterosexual ones are discordant with their twins. Then the correct interpretation is not that a biological basis for transgenderism is found but one for homosexuality.
If, on the other hand, it turns out that 65 of the homosexual ones are concordant and 15 of the heterosexual ones, then the correct interpretation is indeed that a biological basis for transgenderism has been found. However we can not distinguish between these possibilities unless the study explicitly controls for sexual orientation.
Also, do you have a study showing that transgenderism is a possible outcome of homosexuality?
There are a bunch of studies showing that about 80% of transgender youth grow up to be cisgender homosexuals, I could go look for them if you want although a quick google search should find them. Whether that means that transgenderism is a possible outcome of homosexuality, or that homosexuality is a possible outcome of transgenderism, or that there is some other unknown factor influencing both is hard to tell, but that there is a strong association between transgenderism and homosexuality is clear. You can just take a look at the studies you've been linking to as well, homosexuality is vastly overrepresented in the transgender population (something like 80% of transgenders being homosexual, as opposed to like 5% in the general population). This (the vast majority of transgenders being homosexual) combined with there already being known biological markers for homosexuality (both in brain scans and twin studies), complicates studies into biological markers for transgenderism. Hence the need to control for it.