The most obvious flaw occurs at the end:
"It was intended to protect the church from the state, not the other way around."Let's say that in a forward direction, so we can hear it properly,
"the state should not have any protection from the church."Ergo, the church should be able to do to the state (citizens) as it likes.
Of course, anyone trumpeting this meme would object and obfuscate that interpretation. So then, we should ask if they are lying? Or just given to brazen, meaningless hyperbole? Either answer would fit with most proclamations of religion.
The other, not so obvious, flaw is its self serving argument. Though the statement sounds broad, its execution would be most narrow. The writer may claim to want religion at the helm, but in truth, it is not meant to be that general. Give the reins of government to any "church" other than the writer's own, and listen to the howling commence.
This is why the original phrase was written - Jefferson was assuring a group of Baptists that a majority religion would not use governmental powers to infringe on their rights. Religion, generally speaking, wants to multiply. It wants to convert everyone. Part of government's job is to give you the freedom to say no to religion's desire to assimilate you. Government cannot do that if it too has been assimilated.
However, the writer of this meme, and those who post it are of a different opinion. Assured of their rightness, they see no harm in using governmental powers to nudge you in their direction. In their view it is to your benefit - to everyone's benefit - to see religion and life from their point of view. They believe that under the right circumstances- their circumstances - church and state harmony is a good thing.