Yes, pilgrimages were allowed and there was even a bit of a tourist industry for pilgrims. Crusades were of course not allowed, but small groups of pilgrims wouldn’t be a threat,

The Mamluks destroyed the crusader states on the eastern coast of the Mediterranean by 1291, although a crusader kingdom still existed on Cyprus. There were plans for new crusades throughout the 14th century, and Cyprus did attack Egypt in 1365, but in general, there were no further crusades to the Holy Land. If anyone wanted to fight a crusade, they could go to Spain or the frontier with the Ottomans in southeastern Europe, or fight against pagans in Prussia and Lithuania.

The Baltic region was an especially popular destination for English crusaders. The Teutonic Knights, a military order of monk-knights like the Templars and Hospitallers, ruled their own state around Konigsberg and campaigned against the pagans in Lithuania every year. That’s where Henry went in 1390 and 1392 (so this was actually before he became king, in 1399). On his second visit in 1392, he didn’t stay long. It’s not really clear why, but it’s likely that the Teutonic Knights simply weren’t campaigning at the time, so there wasn’t anything for Henry to do. Instead he turned south, to Prague and Vienna, and ultimately Venice.

From Venice he sailed to Jaffa in January of 1393. That’s actually a pretty strange time of year to go on a pilgrimage. It was more difficult to cross the Mediterranean in the winter (roughly November to March), but I guess with enough determination, and money, the Venetians would take you wherever you wanted to go. From Jaffa Henry travelled to Jerusalem, visited the usual pilgrimage sites, then returned to Jaffa and sailed home. He visited Cyprus before returning to Venice, then Milan, then back to England through France.

Sounds pretty simple…we don’t even really know much about his stay in Jerusalem, since it was pretty unremarkable. Pilgrimages to Jerusalem were absolutely allowed and encouraged by the Mamluks in the 13th and 14th centuries. Numerous pilgrims wrote about their journeys, and there were even more who didn’t leave any written accounts. Pilgrims could land at cities along the coast like Jaffa, Acre, or Beirut, which had all once been crusader cities, or they could sail to Alexandria or Damietta in Egypt and continue to Jerusalem through the Sinai desert. Local guides and translators would take them to Jerusalem.

The Mamluk dynasty that ruled in Egypt was originally a dynasty of slave soldiers from lots of different backgrounds. They could be Turks or Arabs, or even from Christian families. But they didn’t always get along with their Turkish and Arab subjects who weren’t members of the Mamluk dynasty, so sometimes the pilgrimage routes were a bit dangerous. There was also the risk of being attacked by pirates while still at sea. Mamluk soldiers would normally protect pilgrims on the roads though. They recognized that protecting pilgrimage sites was good for everyone - if Christians from Europe could come and go safely, then big spenders like Henry Bolingbroke could show up with a small entourage and put money into the local economy.

The Mamluks also knew this was a good way to prevent new crusades. The First Crusade was launched partly because it was unsafe (or Europeans believed it was unsafe) to travel to Jerusalem. In 1393 it had been over 100 years since the crusader states existed on the mainland, but there was still a steady stream of pilgrims. If Christians were allowed to visit Jerusalem, they probably wouldn’t bother organizing a new crusade. Henry and his fellow pilgrims probably couldn’t carry swords or dress as knights, and they probably had to ride donkeys instead of horses - i.e., they had to play their part, they had to show that they were pilgrims and had no intention of fighting.

Henry’s visit did actually inspire him to plan a new crusade once he became king. He apparently believed a prophecy that he would die “in Jerusalem”, but as usual for the 14th and 15th century, nothing ever moved beyond the planning stage. (Henry did end up dying in 1413 “in Jerusalem” - the Jerusalem chapel of Westminster Abbey.)

Sources:

Anthony Tuck, “Henry IV and chivalry”, in Henry IV: The Establishment of the Regime, 1399-1406, ed. Gwilym Dodd and Douglas Bigge (Boydell, 2003)

Nicole Chareyron, Pilgrims to Jerusalem in the Middle Ages, trans. W. Donald Wilson (Columbia University Press, 2005)

Christopher Tyerman, England and the Crusades, 1095-1588 (University of Chicago Press, 1988)

Norman Housley, Crusading in the Fifteenth Century (Palgrave Macmillan, 2004)