Why was it possible for the Confederacy to ship cotton via European ships docked in Mexico?

The Confederacy adopted a policy known as "King Cotton" during the Civil War (1861-1865). The idea was to deny Europe, especially England and France, the cotton imports it needed in order to force them to aid the South. The Confederate leaders knew that French intervention was decisive in the Revolutionary War (1775-1783), and they believed that cotton was the weapon that would coerce European intervention again.
As part of the Confederacy, Texas had to follow the policy laid out by the government in Richmond. But the state's geography was unique because it bordered Mexico. Small Texas towns such as Brownsville had the ability to ship cotton from Matamoros, Mexico. The cotton was then put on foreign vessels and shipped to Europe in exchange for munitions. The business was lucrative and some individuals on both sides of the border became rich. This trade was not without its share of problems, however. For example, bandits often raided the wagons carrying cotton. But the acquisition of weaponry in this manner did help the South; some officials in the Lincoln administration wanted to invade Texas to stop this trade.
In the final analysis, King Cotton diplomacy was a failure. Britain resented the South's aggressive policy, and it would not go to war with the North over cotton. Texas's unique experience shipping cotton helped the South, and it was a decisive factor in the war.

Cotton was an important tool in the Civil War; European nations, particularly Britain, depended on American cotton, and withholding of it was a policy agreed upon as a way of trying to encourage foreign intervention in the war. However, cotton was also a means of garnering much-needed funds, so it was agreed that the Confederate state of Texas could use its border with Mexico to ship out cotton on the understanding that proceeds would be returned to the central Confederate government.
This cotton was shipped from Texas border towns all the way down the Rio Grande to the Mexican port town of Bagdad, where it could be placed upon European ships. The historic European trade partners remained desperate for US cotton, so it was not difficult to find traders willing to take this route.
https://tshaonline.org/handbook/online/articles/drw01