I will have to leave it up to other historians to talk about ancient or modern dignitaries, but I can talk about the medieval period. For the Middle Ages, the Christian, Jewish, and Muslim worlds were well connected across Europe, Africa, and Asia - much more connected than people expect! There were areas where it would be hard or impossible to find a place of worship, but wherever there was a large enough town or city, there was probably a community of fellow believers.

Muslims

The first diplomat I thought of when I saw this question was Usama ibn Munqidh. Usama was a poet from Shaizar in Syria, but he also sometimes acted as an ambassador between Damascus, Cairo, and the crusader rulers of Jerusalem:

“Whenever I went to visit the holy sites in Jerusalem, I would go in and make my way up to the al-Aqsa Mosque, beside which stood a small mosque that the Franks had converted into a church. When I went into the al-Aqsa Mosque - where the Templars, who are my friends, were - they would clear out that little mosque so that I could pray in it.” (Usama ibn Munqidh, pg. 147)

The Templars did turn the al-Aqsa mosque into their headquarters but these must have been unusual circumstances - Muslims typically weren’t allowed to live in Jerusalem when it was ruled by the crusaders. All of their mosques were turned into churches. In the other major crusader cities they sometimes did have a small area set aside for prayer. The Spanish pilgrim Ibn Jubayr wrote that in Acre, the main economic centre of the crusader kingdom (and later its capital, when they lost Jerusalem again):

“Mosques became churches and minarets bell-towers, but God kept undefiled one part of the principal mosque, which remained in the hands of the Muslims as a small mosque where strangers could congregate to offer the obligatory prayers.” (Ibn Jubayr, pg. 338)

But Acre and Jerusalem are in the heart of the Islamic world and there were ancient communities of Jews and Christians there too, so it was relatively easy for everyone to find a place of worship. But what if a Muslim merchant or diplomat had to travel much further away, to places where there were fewer fellow Muslims or even no Muslims at all?

In the 10th century, Ibn Fadlan was sent by the caliph of Baghdad to the Bulgars, a Turkic people who lived on the Volga River far to the north. The Bulgars had converted to Islam and had asked the caliph to send someone to teach them about the Qur’an and Islamic law. Ibn Fadlan first travelled northeast around the Caspian Sea to the land of the Khazars, another Turkic people, some of whom were Muslim but most of whom were not. Ibn Fadlan found it difficult to perform Muslim rituals in their territory:

“No one, merchant or anyone else for that matter, can perform a ritual wash in their presence, except at night when he will not be seen, because they get very angry. They exact payment from him and exclaim, ‘This man has planted something in the water and wants to put a spell on us!’” (Ibn Fadlan, pg. 11)

But the Khazars provided Ibn Fadlan with a place to ritually slaughter a sheep, so he could still eat in accordance with Islamic law.

Further north in Bulgar territory, there was evidently a mosque of some sort in the capital where the khan lived - at least, they had Friday prayers, and a minbar, which is normally found inside a mosque. Ibn Fadlan had to teach them how to recite the call to prayer from the minbar. In another Bulgar town he found a small wooden mosque.

Travelling back south to Khazaria, Ibn Fadlan visited the capital at Atil, where the Khazar khans had converted to Judaism and had built a synagogue. Most of the Khazars, however, were Muslim and Christian, along with some pagan “idolaters” as Ibn Fadlan called them. He estimated that the Muslim Khazars had about thirty mosques. (Presumably the Christian Khazars had churches and the pagans had temples, but he doesn’t mention them.)

Several centuries later in the 14th century, the Moroccan traveller Ibn Battuta visited every part of the world known to medieval Muslims. He found Muslim communities everywhere, from Spain and sub-Saharan Africa in the west to India and China in the east. Like Ibn Fadlan, sometimes he may have thought that the local Muslims on the fringes of the known world were a bit backwards and uneducated, but wherever he went he was never too far from a mosque.

“In every city of China is a quarter where the Muslims live separately and have mosques for their Friday prayers and other assemblies.” (Ibn Battuta, pg. 890)

By “China” he really means southern China, which was well-connected to the Indian Ocean trade routes. Islam spread easily in India, south China, and the islands of modern Indonesia and Malaysia. However, when he continued north to “Cathay” (northern China), he finally encountered lands beyond the Islamic world. In the capital of the Mongol Empire, Khanbaliq (the modern Beijing) there was no permanent Muslim community and therefore no need for a mosque - but at the time the capital was still under construction and there were no monumental buildings of any sort, only villages and fields surrounding the khan’s palace.

Like most medieval Muslims, Ibn Battuta was less interested in travelling through Christian territories. They could cross almost the entire world without leaving the Islamic sphere so there was no need to visit the backwards barbarians in northwestern Europe! He did however travel to Constantinople, which was still the capital of the Byzantine Empire, and which would be completely conquered by the Ottomans a hundred years later in the 15th century. There was no mosque in Constantinople at the time, but it was surrounded by Ottoman territory so there were certainly mosques nearby.

The only other Christian territory he visited was the island of Sardinia, which also had no mosques.