No other country is quite as heterogeneous as the US. And there is a significant history in the US of using restrictions around voting to disenfranchise certain ethnicities. That makes any restriction around voting a sensitive topic in the US.
Proponents of voter ID claim it is needed to prevent fraud, while opponents point out that there's not enough fraud for it to be worth the cost.
Note that countries such as Australia, Canada, and New Zealand also didn't require voter ID. First-world countries that do require ID to vote have systems in place to ensure that getting that ID is easy even for poorer people - such as automatically sending the ID to the voter by mail if the government requires you to report your residence or filing out the necessary forms once, before turning 18.
Depends on what qualifies as an ID and how hard it is to get one. But unless you're actively providing them to people that need them with no extra work or travel on their part then you're going to be discriminating against people with less money or time.
In the case where disproportionately more poor people are of a certain race then it can be seen as racist (as it affects the population of that race differently). If the reason that disproportionately more poor people are of a certain race is because of racism, then a policy that disenfranchised the poor would effectively extend economic discrimination into political discrimination.
Though I tend to think that even if we remove the economic effects of racism such that disenfranchising the poor couldn't be called racist, they would still be classist and should be avoided where possible.