Parts of it are true. The use of female nudity, pubic hair or menstrual blood is called 陰門陣 (Yin-men-chen, or loosely "Pubic Formation" - note the "Yin" as in Yin and Yang). They were believed to be able to cause guns and cannons to malfunction, interfere with supernatural powers or deities, or just generally act as hexes and anti-hexes.

To understand why such beliefs exist, it is important to bear in mind the following: Firstly, the belief and practice themselves came from the Chinese themselves, and they are resulted from an amalgamation of Shamanist, Taoist and Buddhist beliefs, and of course the inherent sexism of ancient China. The first recorded practice of such beliefs is in 1573, where it was used by several ethnic rebel groups (who believes in shamanism) against Ming troops. Thereafter, such practices were recorded on several occasions. It was not a systematized, common thing, but more of a desperate measure usually employed by the losing side. One interesting occasion was in 1642, when the troops of Li Zicheng, fighting against Ming troops, had naked women stood under the walls. The Ming general responded by sending naked monks to their side of the walls. This tactic was aptly called 陽門陣 (Yang-men-chen).

Secondly, the boxers themselves claimed to have supernatural powers. When their "powers" failed against the foreign troops, they had to come up with equally supernatural reasons for it. They blamed the foreigners for employing the Yin-men-chen, and also accused their own female civilians for interfering with the Boxers' supernatural powers. This effectively gave them a pretty good excuse to why they often fail in battles.

Let's look at the claims made in the page one-by-one.

"They grind up people's eyeballs for medicine." This is true at least for the era. The way Catholic nuns would take in orphans, ignorance about how Western medicine works and a concurrent outbreak of disease helped fuel such rumors and led to the Tianjin Massacre of 1870.

"Before going to war, their foot soldiers smear menstrual blood across their foreheads." I found no direct evidence for such a belief, but the Boxers do think the Westerners utilize menstrual blood in a number of ways. During the siege of the Church of the Saviour in Beijing by the Boxers, it was said that the priests smeared menstrual blood on the roof of the church. They also hung up female skins smeared with their feces and menstrual blood around the church and on their cannons. (In some sources they pinned disemboweled pregnant females on their walls.) The Boxers also explained away one of their losing battles by saying their clothes were soaked in menstrual blood by a saboteur.

"Their officers drink goblets of it." Again, no direct evidence, but it was said that the priests of the Church of the Saviour collected menstrual blood in cups and buried them around the premises as an anti-hex against the Boxers.

"They fly flags woven from women's pubic hair over their churches." Correct. The priests of the Church of the Saviour were said to have woven a flag made from women's pubic hair, which they used to command their troops. They also made an umbrella with pubic hair from 360 women.

"And they straddle naked women over their cannons right before they fire them." Correct. The same priests were said to have straddled women (pregnant women in some sources) on their cannons. They also made a cannon with human skin smeared with blood.

The Boxers dealt with these "issues" in a number of ways. One of them was sending in the Red Lanterns, a female-only Boxers group. Since they were female themselves, such tactics have no use on them. The Red Lanterns were also said to be able to walk on water and have healing abilities. Another was establishing curfew for women. They were not allowed to go outside, unless their faces were covered by a piece of red cloth. As mentioned before, this gave the Boxers a handy excuse when they failed in battle - some disobedient women must have sneaked out and caused their powers to fail. Sometimes, the Boxers would execute female civilians for this reason. Women were also forbidden to dispose of their feces/menstrual blood on the streets or in the yards. Some Boxers also tried to simply avoid women. In regards to the Church of the Saviour siege, Empress Dowager Cixi herself approved of sending in a famous monk to help break the foreign Pubic Formation. The monk dressed up as Guan Yu, brought along a crescent blade, and claimed his horse was Red Hare. He said he was possessed by Guan Yu and was ready to charge into the church. He was, of course, promptly shot dead.

If you can read Chinese, see the study "Women’s Body and Warfare: The Re-exploration of Yin-men-chen in Late Imperial China," which goes into detail about the use of such tactics from late Ming to late Qing.