No, the Gulf states do not have gaydar detectors installed at their ports of entry. But if you are a guest worker - one of the hundreds of thousands of South and Southeast Asians who enter the Gulf annually - you may be (or already are) subjected to an intrusive battery of tests to make sure your "gender" matches your anatomy.
Critics refer to "tests of shame" because in many cases, police doctors conduct these bodily exams of individuals detained on the grounds that their attitude and clothing don't match their physical appearance. Kuwait's health minister announced a proposal this week to make the screening for a "third sex" mandatory in his country, and perhaps across the GCC economic zone - which has a notoriously hard time coordinating comprehensive migration policies. Kuwait already has a law in place that allows the authorities to detain and fine anyone "imitating the opposite sex."
The original reporting suggested that the tests would somehow try to determine sexual orientation, which would be impossible to do medically (not that this has stopped countries from listing HIV+ status as a medical reason to bar people entry, with homosexual individuals in mind). But as others then pointed out, the term "third sex" is a particular new Arabic term that refers to people whose behavior doesn't match their gender -- a broader category that includes transgender as well as gay people.
As The Atlantic points out, it's not exactly like a lot of other governments can cast stones. At least 76 countries still have draconian anti-LGBT laws on the books, and even the US, which banned foreigners with HIV till 2009, still has some restrictions (though not so shameful as the 1965-1990 law that specifically targeted non-straight people by listing "sexual deviancy" as grounds for refusal or entry).
The moral panic evident here is very much tied into Kuwait (and the rest of the GCC's) wider anxieties about migration - even expat naturalization is extremely controversial in these societies. Naturalization would put heavy pressure on race relations and the welfare net in the Gulf states, which is of particular concern given that in the smaller countries, immigrants now outnumber indigenous citizens. As Human Rights Watch reported in 2012 (via Paper Bird):
The criminalization of “imitating the opposite sex” in Kuwait is one element of a broader regime of gender regulation that began to take hold after 1992, when tensions between “liberal” and “traditionalist” Kuwaitis after the Gulf War intensified as each tried to establish their status as influential political entities. The battle over women’s rights and role in society constituted one of this conflict’s most prominent arenas, and presented an opportunity for traditionalists and Islamists to join forces. … Given this long-running controversy within government and society over the appropriate roles of men and women, it is not surprising that parliament would turn its attention towards those who visibly challenge these gender roles.
The health and hygiene of migrants seem to be a priority for the Kuwaiti health minister - which may be partly understandable, given the movement of people here, but is creepily paternalistic and also insulting because of the assumption that any immigrant is likely to be a vector for some infectious disease.
The exams will almost certainly not be applied to white-collar Western workers. "The exams are meant to intimidate poor Nepalis or Sri Lankans or Pakistanis, to exclude those who are too recalcitrantly different," Paper Bird notes - their otherness inspiring a great deal of mistrust in their employers. It is about enforcing conformity - conformity in no small measures based on overly sexualized fears about miscegenation and loss of "manliness," and of being "tricked" by men who "aren't men" and women who "aren't women."