I am really sorry to hear about your experience. I know how devastating rejection can feel, especially when it comes from an organization you so much admire and identify with.
I can imagine the decision felt like a judgement of who you are as a person and of your worthiness as a 'real' Effective Altruist. I can tell how important effective altruism and the EA movement are to your identity and sense of yourself and your purpose, and I am sure you put so much of yourself into your application. How could the decision not feel personal?
I hope you know that EA Global's (or any other EA origination's) decision not to accept your application to their conference is NOT a judgement of who you are as a person, or your intelligence, competency, or ability to do good in the world. It is especially not a judgement of your moral worth. It is not even a true judgement of your dedication to EA causes or your value as a member of the EA movement. EA Global, despite sharing the underlying mission of all things EA, to do significant good, is also just an institution, comprised of a whole bunch of employees, with all the institutional priorities, institutional constraints, and institutional complexities of any institution. It is not a god, it does not see you or know you, and it does not have the authority to make any ruling regarding your true worth or value. The decision-making process is both bureaucratic and human. A binary decision from an impenetrable institution conceals all elements of randomness, arbitrariness, and human best-guessedness that goes into all human decision making processes.
No institution can be an arbiter of your worth or your value. I really hope that you can internalize this. You know what your values are. You identify with the EA movement because your values are so strong and you feel so intensely driven by them. Remember that effective altruism is a philosophy and a movement, not a club.
Being an effective altruist means living your life in a way that aims to promote good in the world/universe to the extent that you are able. Qualification entails the dedication of one's time and resources to this goal, not an invitation or acceptance letter or membership card or special club jacket. I am sure you are doing good, and I hope you can continue to do so with confidence in your worth, importance and total validity.
As a note, I am a total outsider here and can presume neither any insider knowledge to the workings of EAG nor the authority from which to be dispensing advice or telling anyone what to do, but it made me very sad to read your account and that of Constance, and this feels right. It didn't feel right to me that this kind of institutional decision can make such good people feel so bad and demotivated, and i just wanted to offer my personal take by way of explanation for why that is, and with hope that it might make your or someone in your situation feel a tiny bit better.
Besides possibly the Catholic Church or other intensely hierarchical religious institution, if you subscribe to that sort of thing. )
It seems to me to be completely valid to acknowledge that there is a real cost to rejection that is felt by individuals at a very personal level. Part of this cost will be the utilitarian frustration of being thwarted from taking advantage of what one imagines could be a highly effective means of furthering one's goals (i.e. doing good), but part of this cost for many people will be the very personal hurt of rejection, and that both can felt at the same time. We are social beings with identities and values that are rooted in and affirmed by community. This is the reason the philosophy of effective altruism has gained traction in calling itself a community and building institutions around that. Community is important to who we are, what we beleive, and what we do. If doing good is central to one's sense of purpose and identity, and one has found in the EA community an identity and moral framework that provides a means through which one can live out one's values, than a rejection handed down by the highly respected leaders of this community will be incredibly painful on a personal level. Our goals and values are inextricably tied up with our identities and relationships.
The psychological cost of rejection is real and i think potentially detrimental to the greater purpose of the organization in so far as it discourages and demotivates people who are driven by a common altruistic purpose, and contributes to a wider sense of the EA community as gated and exclusionary. To the extent that one cares about these costs, I do not see the gain in refusing to acknowledge that the psychological toll of rejection is real, is valid, and is intrinsically bound up with any more purely instrumental costs.