In the customizing, for some of the modules, there are some transactions which allow us to change the type of the system messages, to warning, error, or no message at all. But they work only for some of the specific messages, not all of them! You should check the corresponding customizing menu and check if suits your needs..

Some examples:
OPJB for production messages
OBA5 for CO messages
OMT4 for material master messages

Otherwise, you have to find other work-arounds to meet the requirement to change the message type.

FYI:

Why is the need to restrict to only some of the messages? System divides the messages into 2 categories from business side. Some messages are issued by the processing ABAP program and they cannot be changed. Because the program cannot continue to run without correcting those errors. But some messages do not result in any contradictions for the processing program, but might affect the succeeding operations in that business process.

Here's the example:

For the first case,Advertisement

When creating the production order, we have to enter the order quantity. There's no way thet system can continue if we do not enter the quantity. So there's no doubt that we shouldn't be able to change the error type for this.

For the second case,
When i create a production order, i can create the batch number for the product in the order before saving the order. And the system checks whether i entered the batch number in the order or not. For the production order creation, it's not a must to enter product batch number beforehand. System can save the order. We can create the product batch separately, or even we can create it during goods receipt for order. Therefore, system could allow us to change the message type to error or warning.

If our production process is desingned, so that the person making the goods receipt shouldn't enter other batch number than that entered in production order, we should make the message type error, so that the planner should have to create the batch number during creation. If however, we only create the batch number during goods receipt, we should allow the planner not to enter batch number beforehand... (This was just a fiction example, do not question it, and don't look for this setting in the customizing)