The three churches in my town are of different denominations (Methodist, Protestant, catholic) but they’re all similar architecture (gothic). If you were an architect in 18th/19th century was it socially acceptable to build churches for whoever would pay, or did you have to stay to your own sect?

It wasn't rare to have a skilled member of one religion help make a house of worship for another. In the classical period of the Ottoman Empire, much of the stone work for mosques was apparently was done by Armenian stone masons. This became less common over time, as far as I understand, but continued well into the 19th century especially for particularly grand mosques. The Ortaköy Mosque, a beautiful baroque mosque in Istanbul near Dolmabahçe Palace, was designed and built by an Armenian father and son team, who actually also designed the Dolmabahçe Palace and Mosque. I learned this only because I happened to visit an Armenian church in a nearby neighborhood (Beşiktaş) and they have a little plaque to them because not only did they design and build this small church (in a very different style) but part of the church was built with excess material from those other grand projects! In the diverse Ottoman Empire, many groups occupied ethnic occupational niches, and most of the best stone masons were Armenians.

In terms of Christian Europe, I only know the Jewish case even a little. In London, the earliest modern (post-Jews being allowed to return under Cromwell) synagogues were designed by Christians. For instance, the Bevis Marks Synagogue was designed by a Quaker. Slightly later, James Spiller designed both the (now destroyed) Great Synagogue of London and the Church of St John-at-Hackney. Overtime, as more Jews became architects as Jewish emancipation and ethnic integration continued, it became more likely for a Jew to design synagogues, but very often the boards seem to have sought out the notable architects of the time, regardless of faith.