As noted before, there is no really clear indication yet from the Trump administration as to how the recent EO’s and the legal battle right now could (downstream) affect LGBT asylum seekers.
This particular site, however, “Immigration Equality” seems particularly objective. A couple of questions: it is sometimes possible to apply for asylum more than one year after arrival, such as if one “came out” recently or had trans-related medical procedures recently in the U.S. If asylum is denied, most of the time removal and deportation proceedings are likely to start quickly, according to the site.
It is possible in some cases for applications to be denied if the person could go back “incognito” and live in a different part of the country. But social media activity while in the United States could be relevant.
It is logical to be concerned that the Trump administration could decide to undermine LGBTQ status as a qualifier for asylum (as a “member of a social group”, if this idea is diluted over conservative objections to reliance on “identity politics” as opposed to “conduct”), or “political opinion” (which in my thinking carries more weight). Someone could host an asylum seeker and suddenly learn that the request will “automatically” denied. Then how would the host be expected to behave?
Many media sources use the term “asylum” carelessly, not realizing that to request asylum someone must already be in the country (sometimes with an overstayed visa, sometimes undocumented).
Catholic Review has a major article of asylum requests at the southern border. But it doesn’t make sense to talk about releasing people from detention centers unless there are private resources to support them.
Trump could complicate the rules for being allowed to work or get benefits later. The underlying assumption of allowing an asylum seeker to go “free” is that someone (often a relative) is available to vouch for the person, and provide financial support, as a dependent. But there is no formal recognition of “private sponsorship” as exists in Canada (which applies to refugees). That sounds like a serious logical gap in the system -- the legal responsibilities of hosts.
Furthermore, there is some talk in Trump-land (to borrow from Michael Moore) that "immigrants" (users of any immigration benefit) who overuse public services could be deported, and that those who had helped them could be billed for the benefit -- an idea again that would logically argue for the development of private sponsorship. There is also talk that some organizations that give services (like HIV-related) to some LGBT immigrants could lose funding in the sanctuary cities fiasco, further arguing for private resources.