My understanding is that Jewish communities enjoyed some degree of freedom in the low countries, the US, the UK, and British settler colonies during this time (compared to what they had experienced in the past). There was certainly contact between Jews and Christians in these areas, but I haven't seen any sources mentioning Christians converting to Judaism, only the other way around.
I can't talk about the US, settler colonies and the rest of Europe, but conversions were definitely happening in Britain- usually as the community bonds from immigrant communities weakened. The majority of converts then, and possibly even now, were women, who converted before marrying their Jewish husband- and for many Christian British makes, the conversion process would have been especially off putting as a circumcision would be required. There are records of mostly Askhenazim conversions- the first convert within a British Sephardic community was in 1877. Previously, converts may have gone abroad for conversion, however.
An early conversion, the first conversion known in Plymouth, was outside of your time frame, around 1785, the convert was named Abraham the Proselyte. Why he converted, we can't know, but he had a Jewish son named Joseph that year, and it's possible he converted to marry a Jewish woman or the building Plymouth Jewisj community allowed him more exposure to the faith and community which inspired him to convert. However, the first marriage between a born Jew and a Jewish convert to take place in that city which was entered in the Marriage Registers was in 1890. Before then, converts and their spouses would have had a civil marriage before a religious ceremony which was purely symbolic without legal effect.
We have records of converts within the 19th century across Britain, for example, through 'A List of Converts to Judaism in the City of London, 1809-1816, ed. Barnett A. Elzas', as well as through the London Beth Din records, mentions of conversions in letters to the Chief Rabbi and so on. An idea of a typical convert would be that of Miriam, daughter of Abraham, who converted in Exeter in 1810. 'Bet Abraham' or daughter of Abraham was the patronymic used for converts to Judaism. We know this as it was recorded in a letter to the then Chief Rabbi and it was clearly an event of significance, as all conversions are. Within three years, a family of Jews, also within Exeter, converted within the same congregation. Although we cannot know the full details of their conversion, reasons could be purely religious with all members being converts, or perhaps the father was Jewish, and therefore the mother and children, who needed to convert as they were not born Jewish under Jewish law, converted later. Just a year later, we have records of a Rebecca (daughter of Abraham) who along with her four and two year old daughters, Rachel and Leah, converted to Judaism in September 1814, as she was married to Menahem Mendel Ben Ze'ev Wolf, in Exeter again. Within four years, we have a minimum of two families converting alongside Miriam. The process of conversion is and was a long and difficult process, taking years to complete.
But the majority of conversions we probably don't have English records for, as they took place abroad- in the Netherlands. Why? Perhaps it was easier to convert as local congregations might have been against converts or at least unwelcoming as some congregations are today, or perhaps it was out of fear of reprisals. Although Britain was certainly less anti Semitic than, for example, Eastern Europe, and you could not expect pogroms or anything similar, that doesn't mean there was no anti semitism. An example would be Martha, the wife of Zvi Ben Isaac, who converted in Holland, the Netherlands, in 1872, before they married. Conversions of course did occur inthe Uk, especially under Solomon Hirschell of. London, up until 1835 especially. The Netherlands was traditionally an accepting and safe place for a Jew, with a strong Jewish community.
More on British converts, searching the pre 1851 database on JewishGen, there is an Isaac Barnett, born 1801, dying 1851, in the City of London, who has 'Abraham our Father' under the 'father' section of his ID and underwent baptism. He was therefore a convert, married to a Jewish spouse and buried in a Jewish cemetery. On the 1851 Anglo-Jewry database there are 201 known converts to Judaism or suspected converts to Judaism, including Isaac Barnett. This is not an exhaustive list of those who had died recently or were converts and alive and well in 1851, there were probably many more.
I have got an interesting story of converts from outside Britain- and that's from Russia. In 1876, in the small village of Solodniki, 163 villagers converted to Judaism and left for Israel. There are no surviving records of how they converted- presumably in a nearby Jewish community- or of any reprisals the local Jewish communities faced, although the converts themselves faced discrimination and persecution. Supposedly, Abraham Kurakin was ringing the church bells in the village on Christmas Eve when he received a 'divine message' telling him to become Jewish and to convert. People from the village gathered round and heard his story and clearly were convinced, as a total of 37 families converted, including the Kurakin family, before eventually leaving to settle in the Lower Galilee, modern Israel.
Within Israel, they weren't wholly accepted. Many born Jews disliked or didn't trust them, and they were nicknamed Subbotniks, meaning observers of the Sabbath, forming their own community. Their descendants kept quiet about the conversions and integrated within the community, but the history of their families was rarely or never spoken about, which shows a fear of being unwelcome or not being accepted within the Jewish community.
Another interesting anecdote is about conversions to Judaism in 20th century Western Europe under. Nazi rule. Yeah, Nazi rule. In 1941, in the Netherlands, a chairman at a forum of Chief Rabbis talked about the influx of applications for conversions, specifically in Amsterdam, with demand existing 'in other regions, as well'. The majority of the forum were opposed to accepting converts- Rabbi Levisohn in particular was recorded as saying to accept converts would be a 'mistake', especially considering the 'German legislation' (the invasion of the Netherlands had happened a year previously and anti Semitic laws were in place and rigid). The chairman is recorded as saying 'the general tendency is to accept very few converts'.
In Eastern Europe, Jews could expect to face reprisals and attacks after conversions. Perhaps the most famous Eastern European convert to Judaism was outside your time frame, in the late eighteenth century, but the reason I mention it is that the story became especially popular in the nineteenth and twentieth centuries which can tell us about Jewish attitudes to conversions- and their fears of Christian attitudes. Graf Potocki was supposedly the son of Duke, who was a 'ger tsedek', meaning a righteous convert, along with his friend, Zaremba, who also converted. Most of the story is probably legend.
Potocki studied at an academy in France, when he met a Jewish student who was studying the Torah. Interested, he, along with Zaremba, quit the academy to study alongside the Jew. They were good Polish-Lithuanian Catholics- until they began questioning the validity of Judaism after learning about the Jewish faith. Supposedly, Potocki left to visit Rome, to try and renew his Christianity, but upon discovering the corruption rife within the Papal court, he gave up- and decided to convert. He left for Amsterdam, a safe place for Jewish converts, and underwent the process to become a convert. Potocki left to travel Europe- and disappeared.
Zaremba had not gone with him to Rome, instead returning to Poland, marrying a noble daughter, promising to join Potocki in Amsterdam for conversion. When he heard of the disappearance of his friend, Zaremba rushed to Amsterdam with his wife and young son- converting to Judaism along with his wife and child. Potocki and Zaremba later met up and left together to Israel.
But the reason why this legend became so popular was to happen a bit later. Potocki decided to return to Lithuania, where he was quickly arrested and charged with apostasy. Quickly they realised he was Potocki- the missing son of a nobleman. Lithuanian nobles and clergy tried to 'save' him by making him renounce. Judaism and return to Catholicism, but he refused- and was ultimately convicted and burned to death as punishment. Supposedly, the houses of those who had brought wood to lay for the fire were burnt to the ground in holy vengeance- an attractive ending to the story of the local Jews, for sure. According to folklore, you can find Potocki, known by his title Ger Tsedek, in the Jewish cemetery in Vilna (Vilnius).
The small details developed in the nineteenth century, being mentioned in Jewish literature, told in local folkloric stories, with a known Hebrew, Polish and Yiddish manuscript, dating from the early 19th century, 1841 and 1913 respectively, and there were books based off it- and a popular play by Alter-Sholem Kacyzne, called Dukus, in the early 20th century.
Anyway, to sum up, attitudes to converts to Judaism could be somewhat hostile within the Jewish community, and were also somewhat hostile outside of the Jewish community, although less so in Holland. I wouldn't say they were completely accepted within Jewish communities or outside Jewish communities (especially those who converted under Nazism...) and were probably not very common, but were also definitely not unheard of.
My sources mainly come from the PHC Marriage Register, The Central Archive for the History of the Jewish People, and the Jewish communities series by Israel Cohen about Vilna.
Some sources easily accessible at libraries etc about converts to Judaism would be Sketches of Jewish Life and History by Gersoni, with a whole sectioned dedicated to the 'Converted Nobleman' story above, along with Noble Soul: The Life and Legend of Vilna Ger Tzedek County Walenty Potocki by Joseph H. Prouser, Halakhah and Practice by Menachem Finkelstein and Holy Mystics: Jewish and Christian Dissent in Eastern Europe by Glen Dynner.