Karaite Synagogue

What claims to be the oldest synagogue in Jerusalem or the world (from the Eighth Century, damaged when the old Jewish Quarter came under Jordanian control in civil war in 1948, restored and brought back into use after the Quarter became part of Israel following the Six Day War of 1967) is not part of rabbinic Judaism (the normative form of Judaism which developed in the period shortly before and then for a while after the time of Jesus) but of Karaite Judaism (which follows a strict interpretation of the Torah and rejects all later developments and later festivals).  The synagogue's ancient Torah scroll is written on deer skin.

The Karaite's take off their shoes to enter the synagogue and prostrate themselves during prayers, both of which we might imagine are Islamic practices.  It is just possible that this reflects a common approach to prayer from the period before either modern Judaism or Islam arose, although it is also possible that the customs have developed later independently.  The possibility that they reflect early practice reminds me of other speculation that practices in some Eastern churches (such as a manner of fasting and the use of prayer mats) reveal a common approach to prayer before either modern Christianity or Islam arose.