So the article you linked is just a summary of another summarizing article, itself drawing on the conclusions of an article published in a theology journal: David Tombs, "Crucifixion, State Terror, and Sexual Abuse: Text and Context," originally from the Union Seminary Quarterly Review (53, Nos. 1-2 [1999]: 89-109).

The original article by Tombs is self-admittedly speculative. One of its major points is looking at sexual abuse in violent conflicts and war in modern Latin America, and then suggesting that this points toward a more general prevalence of sexual abuse in the context of political violence — such as in the first century Jewish-Roman War, and in Roman crucifixions and the crucifixion of Jesus in particular. Tombs writes, for example, that

Josephus’s account of the Siege of Jerusalem (War, V. 420-572) suggests that the comparisons between the ancient world and modern Latin American torture practices may be appropriate. Josephus’s description of how the Jewish militants inside Jerusalem tortured the civilian population in the search for food provides a graphic insight into sexual tortures at the time: ‘terrible were the methods of torture they devised in their quest for food. They stuffed bitter vetch up the genital passages of their victims, and drove sharp stakes into their seats’ (War, V. 435). Although the actual historicity of Josephus’s claims can hardly be taken for granted (since Josephus was writing for a Roman audience and his exaggerations and vested interest in casting the Jewish rebels in a poor light affects his testimony throughout his account), it nonetheless suggests that the sexualized tortures of twentieth-century Latin America might correspond quite closely to their first-century Mediterranean equivalents.

As it pertains to Jesus' crucifixion, one important thing he notes is that it's "helpful to distinguish between sexual abuse that involves only sexual humiliation (such as enforced nudity, sexual mockery and sexual insults) and sexual abuse that extends to sexual assault (which involves forced sexual contact and ranges from molestation to penetration, injury, or mutilation)."

Now, we know that forced nudity and insults are an element of the accounts of Jesus' crucifixion as we find them in the New Testament gospels. Tombs then kind of uses this to suggest that this may increase the likelihood of even more extreme sexual abuse here.

The most relevant paragraph is this one:

Depending on the position in which the victim was crucified, the display of the genitals could be specially emphasised. Both Josephus and the Roman historian Seneca the Younger attest the Romans’ enthusiasm for experimentation with different positions of crucifixion. Furthermore, Seneca’s description suggests that the sexual violence against the victim was sometimes taken to the most brutal extreme with crosses that impaled the genitals of the victim. This practice might never have been the case in Palestine—and there is no evidence that suggests it happened to Jesus—but at the very least, it suggests the highly sexualized context of violence in which Roman crucifixions sometimes took place.

As for the first sentence, based on the footnote this, this itself doesn't owe so much to any actual literary accounts or known/deliberate practice, but rather speculation about the position in which Yehohanan was crucified — the well-known first century Jewish crucifixion victim whose ossuary was found in the 1960s, with a crucifixion nail still embedded in his heel. On a particular interpretation of this positioning, "the exposure of the genitals would have been particularly pronounced."

Beyond this, Tombs' argument just seems to rest on Seneca's description of genital impalement.

Of course, anything's possible; though I think the original Patheos article's "[a]nal and vaginal rape were expected parts of that torture according to contemporary historians" is misleading/incorrect with respect to victims of Roman crucifixion — and along with that its conclusion that "not only likely that Jesus was literally raped at some point during His passion – it would be surprising if He wasn’t."