Moreover, if you want to prevent Less Wrong from becoming a cult like the Objectivists, it may be advisable to absolutely avoid to perform rituals explicitly modeled after religious ceremonies, like this or this.

Mmm. I think it's fairly clear that modeling ceremonies on religious rites (or doing much ritual at all outside a certain narrow scope, for that matter) is more likely than the alternative to lead to undesirable perceptions of LW. And PR is important, yes. But I'm not convinced that they're actually epistemically dangerous to any significant degree.

There's a lot of possible reasons to do ritual. The two ceremonies you link seem to mainly fall under the general heading of "affirmation of shared values", which could be used as part of a more general Dark Artsy scheme but don't seem terribly dangerous in themselves; rituals with those aims show up in dozens of secular contexts, from the Boy Scouts to martial arts dojos to the Pledge of Allegiance recited by American schoolchildren. I might have been given pause if it snuck in some seriously controversial content, like a pledge to sign up for cryonics or that believers in the collapse postulate were stupid and also evil, but as long as it limits itself to cheering for a materialistic humanism I don't think there's much to object to. That's way too general to be epistemically risky, and attempts to cast it as such would probably be more funny than menacing.

Now, why pull from a theological source when there's all these other sources available? Well, religions have been doing it the longest, for one thing. In the absence of a deep understanding of the mechanics of something, a good heuristic for getting it done is to find someone that does it well and plagiarize.