Not sure about Jesus, maybe he just made a status move against his competitors, but in general...

Goodhart's Law applies to bragging about donations too -- if you make it a norm, people will optimize for visibility instead of doing good; there will be charities helping them to optimize for this goal... and soon you may get a culture where people donate a lot to charities that actually don't do much good, because most of their spending goes on increasing the visibility somehow.

Taking a wider view, maybe we would agree that maximizing donations to EA is still a positive goal, even if it brings some negative side-effects. But remember that most people don't care about effective altruism, and would consider other charities more worthy. So you might be effectively creating a culture where people get points for publicly donating to organizations that you might find useless or even harmful. (Imagine organizations for effectively spreading a religion, or effectively spreading a totally mindkilled version of a political movement you disagree with.) Now you would be stuck in a situation where you either have to "voluntary donate" money to a cause you hate, or become a visible defector because everyone else around you already made their donations public.

For reference:

Be careful not to practice your righteousness in front of others to be seen by them. If you do, you will have no reward from your Father in heaven. So when you give to the needy, do not announce it with trumpets, as the hypocrites do in the synagogues and on the streets, to be honored by others. Truly I tell you, they have received their reward in full. 3 But when you give to the needy, do not let your left hand know what your right hand is doing, 4 so that your giving may be in secret. Then your Father, who sees what is done in secret, will reward you.

The explanation I heard at church was that the "hypocrites in the synagogues" would act charitable just to get the social status associated with it, but a really chariable person would want to be charitable even if they had to hide it.

I'm not completely clear on who was supposed to benefit from hiding charity. The giver, because they'd be sure they were doing good for the right reason? Or the community in general, because tolerating people who give for signalling purposes would have caused some kind of harm?

I think it's most likely that this is either virtue ethics (so the giver can be sure they're a good person), or an argument from asthetics - getting social status makes charity less asthetic.

It helps prevent holiness spirals.

In most branches of Christianism, status-seeking is frowned upon as part of the sin of pride. By removing braggarts from the equation, only sincere altruists are supposed to be left.

Probably because rich people have most to lose if they're expected to be charitable, and rich people controlled what got published in the Bible. If giving is supposed to be secret then who can prove they're giving nothing?