Victor, please don't go there - makes you an easy target. You don't understand culture from the above statement or the concept of identity for any given member on the forum being made up of multiple cultures. The assumption of a single cultural influence for any of us is a false start.
With every defensive answer, the "Kick me" sign on his back grew........

That's the flavor I'm getting and it sucks. I'd like strawberry instead please and it better have
real strawberries. None of that stuff with artificial flavoring!

So refreshing, you understand!
My #2 pet peeve in this world, after blatant unfairness/cruelty, pretentiousness. Following toe to toe with righteous ignorance.
1. What is culture or identity in the context of an online identity?
I'd say, not very much, if at all. Unless the forum you've joined is specifically about a cultural identity.
For TypeC type forums, I think individuals' cultures become important if:
(1) they need clarification understanding something given the cultural block. Say, English is not their first language, or its a cultural meme that they're not familiar with, etc.
(2) The particular topic of discussion. If it's relevant to cultural identities, then, discussing where one is coming from and all that they know of their own cultures, can add a richness to the discussion.
2. How do we measure or determine how guarded or open one is on an online forum?
I don't even think it's relevant to measure it. Be as guarded as you like, be as open as you like. Your choice.
Just don't mix up the two for your audience. I.e., be guarded, but say you're open. Be open, but say you're a timid wallflower. (unless you're joking

)
It's asking for a reactionary response from the audience........the question that's implicitly asked through such contradictions, is,
'are you buying it?'
Should it measured by the level of personal detail one is willing to offer?
No.
Does a higher level of personal detail imply a greater level of sincerity in reflecting one's RL views/opinions?
No.
For me, it's the genuineness of the discourse that matters from online forums. As, written discourse is our only ties to one another.
Give genuinely to that, don't mask, shape-shift, present false information as truth, muddy facts, etc. And, I don't even care if I believe the position I may be arguing, or if you do........but, I can't explain it, there's still an genuineness, a responsibility to present the thought as openly as possible, and be open to the responses piqued by that thought, which matters to me.
Does the anonymity that is offered to us here (it is a choice, you know at both ends

) provide us a safe space to present our views/opinions openly in a way that the personal details would inhibit us in real life?
Most certainly. I would not be as open as I am online, if I was tied to my tangible identity. As I don't know the people on this forum. Being tied to my tangible identity, and being open is fine and great IRL, as those are my trusted FRIENDS & FAMILY. I can't trust most of the people here, as I don't know who they are. So, of course, I'd just want to be free to share my thoughts without ties to my tangible identity. E.g., I would not want my supervisors coming upon a post of mine discussing how I am turned on by gay men, as a straight female and the intricate details of why I have that taste. But, I love that I can share this online, and have a discourse of this thought of mine, that very rarely do I get to discuss as openly, IRL.
3. Finally, why should this matter at all?
Nope. It shouldn't.
Except........when the person in question is ASKING for it to matter.
I really am x, y, z, BUY ME!! BUY ME!!!!!!!
One then has permission to respond.
Precisely because it's an international forum, distance and details become less important than more. When we don't present our views as tied to particular contexts, we allow people to see us for us - not tied to stereotypical images of the environments in which we reside. More similarities and differences based on personality type - after all, isn't that what brings us here?
Well said.