A neutral word for “ecclesiasticism”

The common definition given for the word “ecclesiasticism” is:

adherence or over-attention to details of Church practice

Take the following observation (slightly paraphrased from the original article):

When ecclesiasticism attempts to address the physical realm, it frequently fails.

With respect to above usage (that theism should not interfere with physical studies, etc.), does the word “ecclesiasticism” always carry connection with Christianity and the Church? Is there a word where I want to make the same point, but without emphasizing any specific religion?

Ecclesia and its derivatives does always carry a connection with the Church, and has done since the word was used in the Gospels and the writings of St Paul.

κἀγὼ δέ σοι λέγω ὅτι σὺ εἶ Πέτρος, καὶ ἐπὶ ταύτῃ τῇ πέτρᾳ οἰκοδομήσω μου τὴν ἐκκλησίαν, καὶ πύλαι ἅδου οὐ κατισχύσουσιν αὐτῆς.

I also say to you that you are Peter, and upon this rock I will build my Church; and the gates of Hades will not overpower it. (Mt 16:18 NASB)

τῇ ἐκκλησίᾳ τοῦ θεοῦ τῇ οὔσῃ ἐν Κορίνθῳ, ἡγιασμένοις ἐν Χριστῷ Ἰησοῦ, κλητοῖς ἁγίοις, σὺν πᾶσιν τοῖς ἐπικαλουμένοις τὸ ὄνομα τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ ἐν παντὶ τόπῳ, αὐτῶν καὶ ἡμῶν:

To the church of God which is at Corinth, to those who have been sanctified in Christ Jesus, saints by calling, with all who in every place call on the name of our Lord Jesus Christ, their Lord and ours: (1 Cor 1:2 NASB)

To my knowledge the word has not been claimed by or applied to other religions.

A suitable alternative might be religiosity, or your own theism.

religiosity: Strong religious feeling or belief. (Lexico)

theism: Belief in the existence of a god or gods, specifically of a creator who intervenes in the universe. (ibid.)

Lexico points out that theism differs from deism:

deism: Belief in the existence of a supreme being, specifically of a creator who does not intervene in the universe. (ibid.)

[It's a pity that certain implementations — maybe all implementations — of Georgia don't contain all accented Greek characters. What appears as ὼ for example should look like ὼ.]

Ecclesiasticism is a particular branch of Christianity that lays emphasis on organised church practice. Not all Christians are practitioners of Ecclesiasticism. Not even all Christian organisations practice Ecclesiasticism.

The word derives from the Greek for church, meaning a religious congregation or community rather than a building. As such it will be assumed to refer to Christianity.

If you want to expand the word to include other religions you will have to find the names of equivalent groups within those religions, or else make it deliberately inclusive. Such as saying "Ecclesiasticism and its equivalent in other religions".