Does the beauty of Buddhism lie in letting seekers seek beyond the bounds of religion?

Beauty is the third liberation.

AN8.66:3.1: They’re focused only on beauty. This is the third liberation.

There are seven other liberations, some before, more beyond.

Possibly so.

I was taught Roman Catholic doctrine ("cathechism") as a child, and that was of a variety which was old-fashioned even then. I found it was unobjectionable -- I didn't believe it, necessarily, but I didn't object to it -- except for their doctrine that "only this is true" ... i.e. that only the Church's doctrine is true and that everyone else is wrong (the Church's doctrine seems to have changed a bit since then, though that's off-topic here).

At the time, I refused to believed that ("every other doctrine is wrong"), and consequently I read the books of other religions eventually including about Buddhism.

Buddhism too has passages which say things -- like MN 11 -- which imply that Buddhism is true, and that only Buddhism is true (not that I'm trying to refute that).

But it's also said of the Dhamma:

Svākkhāto bhagavatā dhammo:
The Dhamma is well declared by the Bhagavā:
sandiṭṭhiko akāliko
visible here and now, immediate,
ehipassiko opaneyyiko
inviting to come and see, effective,
paccattaṃ veditabbo viññūhī ti.
to be individually ascertained by the wise.

I think there are people who understand that as meaning that the Dhamma is true by definition because it is (by this definition) that (portion of it) which is visible and evident and effective and "individually ascertained by the wise".

And so (to tie it into your question) it is "beyond the bounds of religion" -- i.e. it's practical etc. -- if by "religion" (as opposed to e.g. "science") you might mean, "that which can only be an article of faith" (see also for example What are the differences/similarities in the concept of faith as used in Buddhism and Christianity?).

We're also told that Buddhism is a "gradual training" -- maybe starting with "be kind and don't kill people" and working it's way on up from there.

There's also this quote from the Dalai Lama which you may or may not appreciate, to understand in context.

Where else can a seeker go but yonder past a certain point?

Um.

Well ok. Maybe that was a rhetorical flourish rather than a question but there's something to do with maybe stopping seeking. There's a Brahmana Sutta (SN 51.15) where the protagonist suggests that the path is endless, and Ananda replies that it ends "when you reached the park".

As a footnote I think that, in that sutta, "the park" is where they were -- "at Ghosita's Park" -- and that "park" can be understood as "forest monastery" i.e. before there were big monastic buildings, the monks in the forest or wilderness or in parks which they were given to use (perhaps by rich land-owners or kings).

There's maybe also something to do with no longer seeing yourself as a seeker -- or seeing "seeking" as a "yourself". MN 11 for example lists four kinds of grasping ...

The Realized One, the perfected one, the fully awakened Buddha claims to propound the complete understanding of all kinds of grasping. He describes the complete understanding of grasping at sensual pleasures, views, precepts and observances, and theories of a self.

... of which I think "I am a seeker" might be one, i.e. one of innumerable examples of a theory-of-self: whereas, conversely, Buddhist doctrine includes anatta.

If you want to make this a comparative-religion question (which perhaps you don't) other religions might have doctrines which could be compared to anatta -- like Christian unselfish love or Islamic mindful obedience. Buddhism (at least as it's explained in the suttas) more-or-less does without "God" though, so, yes, in that sense, "beyond the bounds of religion".

When I was young I was told by a booklet that if I found a better religion, I can follow that one.
Yes! allowed as per human rights.
As per buddhist scriptures, " Respect other philosophies, compare them with my(buddha's) teachings and follow me only when you find my teachings to be better ".

I liked the idea of God centered, open-sourced religion back then so it was what kept me loyal
Good, because sometimes(most of times, to be precise) philosophers dwelling in thoughts about anatta start breaking 5 percepts at mental level and become dishonest to closed-ones at body-speech level.

•••and the reason I found out that there was more to know beyond it.
Good, because your behaviour seemed to satisfy you and others in doing so. It doesn't mean that there is anything more to know beyond anatta.

Where else can a seeker go but yonder past a certain point?
Theoritically, as per buddhist scriptures-- when seeker stops even seeing/feeling/realizing h-im/er-self as 'seeker', when a state is reached where, "causes&conditions are interacting with causes&conditions", then
What seems to be yonder stops seeming because there is/was nothing to yonder to from the start.

Does the beauty of Buddhism lie in letting seekers seek beyond the bounds of religion?
Finally, yes if religion is binding you with 'Ignorance' of some atta.

May you be free from your confusion.
Metta.