I agree with your first statement. However, this is one case where we don't have to make any guesses. City voting records are public.

If you actually checked, then you'll see that Democratic and Republican controlled cities have seen an uptick in murder rate. In some cases, Republicans have a higher increase. So this isn't an issue with any particular party.

> in many countries, urban areas are less violent

This might be because of better mental healthcare, less drug/gang related violence, better gun control, or a variety of factors. If America had the same laws as other countries then this discrepancy would be strange however the US has been very slow at getting up to the current standards that most developed countries have adopted.