All people naturally crave approval—this is often hidden but powerful. Self-approval is included in this.
Even heroic acts or great sacrifices are usually motivated by the desire to be seen, remembered, or honored. Being seen doing good is often a reward in itself; people may not want praise, just recognition. Religion or spirituality amplifies this by introducing the ultimate observer—God.
But...
Just because people want approval does not mean they would refrain from doing a good deed unless they get approval or have it in their sights.
We do not know how significant that is. It could still be the case that a
person acting without being motivated by the wish for approval is extremely
uncommon.
Also, if you only consider the human level, it could be a very high number that
has the motive of obtaining approval. The number will be higher still if those
people believe in a loving God.
We would need evidence before assessing anybody as having done a good deed without self-interested approval.
People will more likely than not, perhaps invent a God to approve of and who approves of them in return.
Man prefers man's word to God's and likes his word to be taken for God's. Even if a person seems to be totally God-centred they might not be. Many pagan idolaters could have been champions where devotion was concerned.
The truth can coincide with what you want to believe. It is possible to serve the truth not because it is the truth but because it is what you want to hear. That is not real service of the truth. So even if the word of God were correct, it would not mean you care.
It is safe to assume that people approve of themselves so much that they have to invent a God to reinforce and represent how great they are.
Religious practices such as confessing sins and getting forgiven are often just self-approval games. You can be proud of being humble. Getting easy forgiveness is a sign of self-approval. "I have such great sincerity and potential that God forgives me easily. I heal fast."
Here is how the Mayo Clinic research group defines narcissistic personality disorder. It is “a mental disorder in which people have an inflated sense of their own importance and a deep need for admiration. Those with narcissistic personality disorder believe that they're superior to others and have little regard for other people's feelings. But behind this mask of ultra-confidence lies a fragile self-esteem, vulnerable to the slightest criticism.”
Faith in a God who approves of you and admires you is a form of this disorder.
Because this is about that God and you, the people around you may not notice that there is anything wrong.
If you admit you love God and only worry about people for his sake then that is a way of not caring about others' feelings - though it may not lead you to harm them. You just happen to act as if you care for them. If this God is based on your ideas about him, your wishes, it is not a real God but your perception. The real God is you.
The person who benefits from your "love" will sense that they are being used to please a projected God. That is quite cruel especially if it is a vulnerable person who just needs to be just loved.
The giveaway will be the hatred you feel for anybody who seems to challenge or explicitly not share your faith.
Self-esteem, when it is about what other people think of, can be fragile. It is always in danger. There is no reason why the same thing cannot happen if you base it on God. It will often be worse for you will have more to fear from a God who you think exists, than people for he is all-powerful. Hating what you think God thinks of you will lead to you taking it out on people especially the easy targets.
Conclusion:
Doing good for approval—especially divine approval—is not true goodness. If you truly believe that approval-seeking spoils moral action, you must reject belief in God, since that belief fuels and worsens the craving for approval. True virtue demands detachment from rewards, recognition, and imagined divine applause.
APPENDIX - THE IRONY!
Jesus said that you must not let your right hand know what your left hand is doing when you help another person.
When you help, you are supposed to do it because God says so or because it is right - and not because you want approval.
The atheist will say, "When you help, you are supposed to do it because it is good - and not because you want approval or because anybody commands it".
Is doing something because it is right just another way of saying you are doing it for the approval? Not necessarily. But doing it because a God commands it certainly is.
If you can hide your good work from the person you help and don't, then you are looking for approval from the person. The believer should wish that God cannot see. But that would amount to admitting that God is not clearly a moral idea - it is mixed at best.
A religion preaching selfless service towards God and saying it does not seek God's approval as a reward in itself, does not mean the religion can or does live up to it.