Some might think that sincerity simply means that you do something in secret or you hide your actions from people. Although that is somewhat true, I don't think it's the whole picture. Sincerity might not be that simplistic.
You could be hiding your actions, but still be insincere. How? For example, if you hide your actions such that you want people to call you sincere or humble or righteous. In such a case, you're not sincere.
On the other hand, you could publicize your actions but still be sincere if the publicity doesn't matter to you. In such a case, you are considered to be sincere right? Even though the whole world knows what you did.
So is sincerity simply means hiding our actions? That could be a part of it, but it is not the defining characteristic of sincerity. I think the defining characteristic of sincerity is in the intention.
If we intend to do it for none other than Allah, then we are sincere. It doesn't really matter if we publicize it or not, because the true measure of sincerity is in the intention. It is in the heart, beyond the sights of people.
Our state shouldn't change whether we publicize it or keep it secret, because we don't do it for any type of recognition from people. We do it for Allah, and He is present whether we are in public or in private.
That is sincerity.
Having said that, another question arises: can we know if someone is sincere or not? Since we already established that sincerity is in the intention, so in the grand scheme of things, we don't really know for sure. We can't say with 100% certainty about a person's sincerity.
However, what is in the heart can show on the limbs. Meaning, it is possible that we can see signs of sincerity. But again, these are just signs. They point towards a possibility of sincerity. At the end of the day, we cannot know for sure. Only Allah and the person know that.
What's my point?
I just want to highlight the idea that sincerity might not be as simplistic as not publicizing our actions. Therefore, we shouldn't be quick to conclude that a person is insincere just because he or she publicized something on social media.
On the other hand, we also have to keep in mind how tricky sincerity can be, because it is tightly linked to our intention. Just like the Prophet's prayer, our hearts is tossing and turning.
"O Turner of Hearts, turn our hearts to your obedience." (Muslim, no. 2654)
Meaning, our intention can change from moment to moment. One moment we might be doing it for Allah. The next moment we might be doing it for something or somebody else. So we have to guard our intention securely and always review it closely from time to time.
Whether we want to hide an action or publicize it, think twice (or more) about why we are doing what we are doing, and be honest about it. If we are doing it for Allah, then the people around us shouldn't affect our actions.
Lastly, don't be so quick to label people as sincere or insincere, because we don't have the concrete evidence to prove it. We can have good thoughts about people and thinking that they are sincere. Obviously, good thoughts about our fellow brothers and sisters is highly encouraged.
But at the end of the day, we don't really, truly know what is in a person's heart. I am not encouraging people to post everything they do online, nor am I encouraging people to keep everything a secret.
If a person wants to publicize a good deed that he did, then let him be. Think good of the person. If a person wants to keep it a secret, then leave him alone. Think good of the person.
Their sincerity is their business. As people who care, we can advice them. But we shouldn't assume anything about their state, since we don't know the reality of it for sure. If we don't know, then we shouldn't act like we know.
Avoid focusing too much attention on something we can't know for sure. We can't know for sure what is in their hearts. But, we can definitely know for sure what is in our own hearts. So perhaps it is better if we focus on that instead.