Some of these are greatly improved, especially the new bold designs and the various colored crosses. The Andean religion is also much nicer.
As far as background shapes, yeah it would be hard to make a system that doesn't impede the different icons. Circles for the Abrahamic is the only thing that really stands out to me as doable, though you already have rectangles behind several of the East Asian religions, and the one Hindu Shakti triangle looks really cool in my opinion.
You might want to find a programmer to help with the city screen and other things, because they are what could really transform this mod from a resource of excellent icons to a must-have revision of the entire religion system.
The Family, Faith, Faction thing is especially high on my request list, because it enables historically accurate civic choices. Take Islam for example. Currently, the game has one version of Islam and one civic (Theocracy) that blocks out the spread of other religions. This is the closest the game comes to replicating the religious policy of the Ottoman empire and many other Islamic states in which Islam is endorsed, other monotheistic faiths are allowed but prevented from spreading, and other religions are exterminated. If you introduce four versions of Islam, then Theocracy is no longer even an approximate replication of the historic stance, since you could only outlaw all other forms of your state faith as well as all other religions.
If we had the Family, Faith, Faction system, then our options become much more colorful. You could choose a civic which allows the spread of Family religions that match your State Religion. If you had Judaism, Christianity, Orthodoxy, and Sunni Islam could spread, but not Hinduism. If you had a civic which only allows the spread of Faith religions that match your State Religion, then a civ with Protestantism could allow the spread of Catholicism and Coptic Christianity while excluding all forms of Islam and Judaism. Finally, if you chose a civic which allowed Faction religion only, then like Theocracy, your State Religion would be the only one allowed to spread.