TL;DR, disclosure and epistemic status
I did a personal shallow investigation on iGEM and biosecurity and could not confirm that the project is particularly concerned with this subject. However, I did find their content on responsibility. I must emphasize that I'm no expert in the field, and haven't consulted an expert on this; that's why this is a question, not a statement. My tentative conclusion is that, if iGEM is indeed concerned with biosecurity, it'd better display that on its main website - so that other people won't misquote them.
(It's hard to me to quantify how much time I spent writing this post, as it includes talking to people to gather opinions on the subject. If I include all of this, I estimate it took me around 3h - 5h to complete it)
What is iGEM
According to the website of the International Genetically Engineered Machine (iGEM):
iGEM educates the workforce and the leaders of the Synthetic Biology industry. The iGEM Foundation is an independent, non-profit organization dedicated to the advancement of synthetic biology, education and competition, and the development of an open, collaborative, and cooperative community.
A friend of mine told me about iGEM competitions some days ago; a bright young scholar she recently met had told her it is a promising investment for EAs concerned with biosecurity. Indeed, I searched for "igem" on this forum and found it has been recommended by hardcore EAs (e.g.: Project Ideas in Biosecurity for EAs), as it is possibly a high-impact organization; another post celebrated that two iGEM members  have co-authored a paper posted on SSRN about the feasibility of on-site verifications of compliance with the Biological and Toxin Weapons Convention (BTWC).
Moreover, according to CSER's new book The Era of Global Risks (Ch. 8):
Intrinsic to the process of engaging in the competition is analysis of the social impact, biosafety, and biosecurity implications of the students’ projects; these aspects are evaluated with the same rigour applied to the scientific components of the work. [...]As stated on iGEM’s webpage: “We foster a community that is mindful and responsible about the development, application, and impact of their work, both inside and outside the lab”.
The reference for this quotation is <igem.org>; indeed, I googled it, and found an identical reference on The Transcriptome.
However, there is no such a sentence on iGEM's website.
Maybe it was cut-off by mistake? Well, I searched for safety-related words on websites with the domain <igem.org> and, indeed, found a beta version webpage from 31 Jan 2022 about biosecurity on <old.igem.org/Safety>.
This suggests that the content on safety was migrated from the main website to the wiki portals of the community, projets, competition, etc. Accordingly, their portal of the iGEM Competition contains information on safety policies , and the wiki on responsibility is more focused on this subject (I couldn't take the time to evaluate it, though). Finally, I used their search engine to look for projects on biosecurity in the last year's competition and to look for content on safety, security, ethics, responsibility, etc. on their blog - and found nothing.
The webpage containing their vision also mentions "responsibility" while talking about "values in practice", but it remarks that
This is iGEM’s next purpose: to make sure that the field of synthetic biology, and all the power that this technology holds, gets developed everywhere by everyone.
That's their own emphasis. All the power, for everyone, everywhere.
Finally, I took some minutes to look for papers associating iGEM and biosecurity; indeed, there is this Biosafety Considerations of Synthetic Biology in the International Genetically Engineered Machine (iGEM) Competition from 2013. They conclude that "Although the students' safety awareness has improved, certain gaps must still be filled before iGEM can fully live up to its role as an educational competition." I ended up way more optimistic when I found the iGEM and Gene Drives: A Case Study for Governance (also co-authored by those two iGEM members), which relates how iGEM developed a gene drive policy after an undergrad team from the University of Minnesota attempted to develop a drive as their (pretty cool) project in 2016: "iGEM did not realize the team was working on a gene drive until the team arrived to present their project at the end of the competition".
I started this shallow investigation a bit skeptical on iGEM's concern with biosecurity, because I could not validate some claims regarding it. I did become more optimistic as I grew more familiar with Millet and Alexanian's work - and yet, this only confirms that people associated with the Safety and Security Program focus on biosecurity, not that iGEM as a whole reflects this consideration.
As I mentioned above, biosecurity is not mentioned as a priority, and it apparently conflicts with their overall goal of "All the power, for everyone, everywhere". This is possibly a matter of "marketing", not of "culture", and could be easily solved by amending its webpages to put more emphasizes on safety. We shouldn't regard this as a minor "optics issue", though; if the iGEM community (and biotech in general) wants to “promote a culture of trust, accountability and responsibility”, it should not only have incentives "to behave in a responsible and safe way, but to be seen to be doing so" - as mentioned on Ch.3 of CSER's new book (by L. Sundaram). Or else, it should be harder for EAs to recommend it.
I shouldn't need to read M&A's work to become more optimistic; and I shouldn't have to trust that they represent the view of their community as a whole. In the world where iGEM is publicly seen as concerned with biosecurity, a post like mine wouldn't have been written - believe me, we all have way more to do.
 Two co-authors were linked to iGEM: Piers Millett, who is also affiliated with FHI, and Tessa Alexanian, an EA and an Open-Phil grantee who led iGEM’s Safety and Security Program. Both of them have other publications on biosecurity and synthetic biology governance. The other co-authors were linked to Universities (one of them also belongs to FHI) and displayed no affiliation to iGEM. My impression is that I can't confirm that iGEM played any causal role in the writing of this paper - unlike the paper on Gene Drives, which was reportedly written because of a project presented to the iGEM raised some flags.
 International Genetically Engineered Machine (iGEM) Competition. Shifting gene drives into reverse: now mosquitoes are the yeast of our worries. Accessed August 31, 2021. http://2016.igem.org/Team:Minnesota