The console messages you see are warning messages. These are triggered for the Third Party tags which are hosted through DTM. As DTM hosts these tags using the document.write, browser issues a warning on slow networks that the script might be blocked. Unless you see actual blocking error message, it doesn't have any impact.
This is isolated to Chrome browser as they have this feature in place to issue warnings and flag such scenarios. However, seeing the architecture of DTM, there is not much that can be changed to avoid such warnings. In case you see actual errors being triggered which blocks the script, we would need an action plan which would include steps to minimize the script and optimize the load times.