Does "God willing" have a religious connotation to it? What are some other phrases that mean the same thing but don't have this connotation?
"God willing" means "If God allows this to be so," so it has a religious connotations.
Other phrases that do not have religious connotation include "If Fate decrees", and "If the wind blows right", or "Hope its my lucky day", all of which relates to the future, but does not have the religious connotation "God willing" has.
How about the expression knock on wood.¹
One of the origins for the phrase "God Willing" or the Latin deo volente is in the Bible from the letter of James 4:14-15
14 Yet you do not even know what tomorrow will bring. What is your life? For you are a mist that appears for a little while and then vanishes. 15 Instead you ought to say, “If the Lord wishes, we will live and do this or that.”
The phrase "God willing" is of the type of phrases that are added so that the speaker does not jinx their good luck by speaking to freely about it.
So, equivalent godless phrases are other kinds of protective magic against the envy of demons (like knocking on wood).
I don't know if there are many people who want to avoid using a religious phrase, but need to protect against demons, though.
it's the direct English translation of the Arabic phrase Inshallah
The word Inshallah (Arabic: إنشالله), also spelt in various other ways, ("Inshalla"; "Inshala"; "Inshaa'Allaah"; Ishallah), is a transliteration of Insha'Allah, (the Arabic: إن شاء الله) meaning "God willing".
so in Arabic-speaking countries, it could have a religious connotation
I'm a Muslim and an Arab, the word "inshaa Allah' 'إن شاء الله' means ' If God Wills' . It's like saying " I'm gonna visit you tomorrow inshaa Allah". It means I am gonna visit you tomorrow if Allah wills.
This is because we don't know the future, only God knows and everything is under his control and his will.
We say this expression because it is in the Quran, the holy book of Islam when Allah commanded prophet Mohammad (pbuh) to say it in these verses :-
(18:23) "And never say of anything, "Indeed, I will do that tomorrow," "
(18:24) "Except [when adding], "If Allah wills." And remember your Lord when you forget [it] and say, "Perhaps my Lord will guide me to what is nearer than this to right conduct." "