Is it permitted to make a church into a synagogue?

Shalom, Thank you for your question. This issue is discussed at length in the early Rabbanic writings. See for example the Mishna Brurah (154, 45) where he quotes an argument between the Magan Avraham and the Eliyah Rabba on this issue. The modern day Rabbis also address this question (See Igrot Moshe, Orech Chaim, volume 1, 49 for example). The issues addressed include whether the building itself was used as part of the church worship (for example when statues were places on the walls, or images were engraved on them), and also the question as to whether it is proper that a building that housed non-Jewish worship now be used as a synagogue, or whether that is unseeming. The Rabbis discuss these questions at length – and each case seems to have its particular ruling. For example, there is a difference between different types of churches (those with statues and those without). There is a question as to whether the building was used for something else in the interim – or if it goes straight from being a church to a synagogue. Also, whether the building is still know as, and referred to as a church. Rav Feinstein zt”l mentions a difference between those churches already turned into synagogues (who relied on the lenient opinions) – which he allows, after the fact; and as to whether one should act so in the future. There are also questions as to whether one is purchasing or only renting (which is more problematic). (See Piskay Tshuvot 154, 30). In short – the answer to you question is not so clear, and each case should be examined by itself by a competent Rabbi. Blessings.