Both.
It hurts nothing.
If you have enough sun to keep batteries charged while you use power, then use only the solar. The solar controller might be better at monitoring the batts than your charger. It all depends on which charging system is better.
Generally I never have my converter on during sunlight. Only at night if I am running fans or TV or something. I just do not need any more than a sunny day gives the panels...
There is nothing wrong, no danger in running both charging systems. You could even run 3 if vehicle alternator is running, still no issues.