To give a more serious answer, Bajorans seem very theocratic and I think most of them would fundamentally disagree with the concept of a secular government.
Bajor exists in a weird gray area since their religion is in some ways literally real. In some ways the Bajorans are like the Vorta and the Jem’Hadar. Their “gods” are provably real, they interact with them regularly, and they have demonstrated to them that they have what seem to be supernatural powers.
Also, critically for the Bajorans, not only are their gods real, but their demons (Pa Wraiths) are real as well. And that opens up a whole other philosophical can of worms. In a way it reminds me of Warhammer 40k. In that universe, religion isn’t irrational. In fact it’s completely rational. Because Chaos is real, and it will fuck you up if you aren’t religious.
Could be because one is a religious symbol and the other is a cultural symbol. There is a case to be made that government personnel shouldn’t be allowed to openly display their religious affiliation in a secular society, in order to preserve the separation of church and state. Not saying I agree with that perspective, but it is a hot topic of debate in many parts of the world today.
And what omelet is that exactly? I bet you 48 hours from now there won’t be a single answer from someone to whom OP directed their question. Nothing can be gained by simply ranting in the interrogative.
I could ask the same question about people who post bad-faith leading questions on asklemmy with the sole intent of ranting about something that annoys them.