Interesting.

There is, however, a disconnection:

In all the countries, once the average education becomes the highschool, the total fertility rate drops to 2.

No connection in Muslim countries, 2-3 children is normal

you're showing two graphs with (supposedly) the same data, but they're looking very different. Can you clarify that?

And then, there's a general problem: the "Western" category uniformly has a education index >7. As you showed above,

After the 0.7 mark, it becomes irrelevant

If that is the case, how can we compare this group to the muslim/christian groups with most members below 0.7?

What I see is this:

• education inversively correlates with religion. No surprise.
• education correlates with GDP (up to a certain treshold)
• TFR (up to a treshold) correlates with either of them

Your conclusion:

Both education and family planning are purely guided by religion/culture/ lifestyle once the basic education and income are provided.

is only the half truth. Education/family planning are indistiguishable for countries with a education index above 7 regardless of culture, religion or GDP. before that, religion/GDP/education and fertility all go hand-in-hand and it's impossible to say which one causes the other, as they are linked.

But for sure, GDP is not the sole factor in fertility, there you are right.