That seems needlessly inflammatory.
The rate of spontaneous mutation in humans is on the order of 10^-8 per haploid base-pair per generation. A few references: one (a blog post summarizing multiple academic papers), two (I think this is one of the papers cited by the foregoing), three (older; rate is ~2x higher), four (intermediate in age and also in estimated rate).
A given gene is many base-pairs long. Accordingly, the "per locus" mutation rate -- which you can think of as how often a particular gene goes wrong, treating all its failure modes as equivalent -- is on the order of 1000x higher. (This, I take it, is where the ~3x10^-5 spontaneous rate for achondroplasia comes from.) The usual cited per-locus rates are, accordingly, on the order of 10^-5, typically a bit lower; see e.g. one (a textbook, which specifically mentions achondroplasia and gives some reasons not to take its rate of spontaneous occurrence too literally as a per-locus mutation rate), two (old paper by J B S Haldane, mostly of historical interest now), three (journal article).
Which figure is more relevant in a given case depends on whether it's one where messing up a single protein, no matter how, causes the effect you're interested in (which seems to be the case for achondroplasia) or one where a very specific change is needed. Which is more likely for homosexuality? I've no idea; more likely than either, I'd have thought, is that sexuality is complicated, that there are lots of genetic changes that can affect someone's propensity for same-sex attraction, and that treating homosexuality as the result of a single genetic change is just wrong.
Anyway, to summarize: no one, so far as I can tell, says that 10^-4 is "the standard rule-of-thumb mutation rate", either per locus or per nucleotide; 10^-8 is roughly the right figure per nucleotide; the right figure per locus is more like 10^-5; which of these figures, if either, is most relevant when considering homosexuality is unclear but for any remotely credible figure it's clear that most homosexuality is not the result of spontaneous mutations.
[EDITED to fix a typo.]
Epistemic status: speculating about things I'm not familiar with; hoping to be educated in the comments. This post is a question, not an answer.
ETA: this comment thread seems to be leading towards the best answer so far.
There's a question I've seen many times, most recently in Scott Alexander's recent links thread. This latest variant goes like this:
Obligate male homosexuality greatly harms reproductive fitness. And so, the argument goes, there must be some other selection pressure, one great enough to overcome the drastic effect of not having any children. The comments on that post list several other proposed answers, all of them suggesting a tradeoff vs. a benefit elsewhere: for instance, that it pays to have some proportion of gay men who invest their resources in their nieces and nephews instead of their own children.
But how do we know if this is a valid question - if the situation really needs to be explained at all?
For obvious political and social reasons, it's hard to be sure how many people are homosexual. Note that we are interested only in obligate homosexuality - bisexuals presumably don't have strongly reduced fitness. The Wikipedia article doesn't really distinguish obligate homosexuality from bi-, pan- and even trans-sexuals. The discussion in the SSC comments used an (unsourced?) range of 1%-3%, which seems at least consistent with other sources, so let's run with that.
The rate of major birth defects in the US, as reported by the CDC, is also about 3%. This counts both developmental and genetic problems, and includes everything from anencephaly (invariably fatal) through Down syndrome (severe but survivable) to cleft palates (minor). But most of these, at least 1.5% of births, were always fatal before modern medicine, and many of the others reduced fitness (via mate selection, if nothing else). Various other defects and diseases, which only manifest later in life, are also thought to be influenced or determined during early development. And so is sexual preference.
(Whether homosexuality is a developmental disorder is not the point; I'm comparing the effect of selection pressure on fatal teratology with its effect on reduced-fitness homosexuality.)
Embryological development is a complex and fragile process, and there are many ways for it to go wrong. We don't wonder how it is possible that selection pressure allows anencephaly to occur in 1 in 4859 births. There are certainly direct causes of anencephaly, explanations of why it happens when it does, but (I think) we don't a priori expect them to be due to tradeoffs yielding benefits elsewhere. It's just as plausible that the tradeoffs involved are against even worse (counterfactual) problems elsewhere - or that there are just no available mutations that don't have these or equally severe problems.
Could it be that linking sexual preference to the biological gender is, for some complex developmental reason, fragile enough that it goes wrong despite all selection pressure to the contrary, that it has no redeeming qualities from the viewpoint of evolution, and that is all there is to it?
When faced with any phenotype with reduced fitness, how can we judge if there is something to be explained - a beneficial tradeoff elsewhere to search for - or merely a hard problem evolution couldn't solve completely? And is there a way to quantify this question, relating it to the known mathematical models of genetics?
Notes:
1. I'm posting this in the spirit of recent suggestions to post more and accept lower quality of (our own) posts to Discussion.
2. I'm going to sleep now and will start replying to comments about 10 hours from now; sorry for the inconvenience.