I’ll admit I lurked a bit to see if you’re US- based and it looks like you are. Maybe instead of “Jesus Christ” you can use “Abraham Lincoln?”
Like “Abraham fucking Lincoln in a cabin made of shit logs” could be a satisfactory expression of frustration.
Any name you can remember easily could work; Billy Crystal, Woody Guthrie, Greta Thunberg, even your neighbors or pets’ names.
The others will be a bit tough since they’re so ingrained in our culture but depending how “non-religious” you intend to be you can switch to “curse/hex” and wean yourself off of that into something more secular ¯\(ツ)/¯