So normally to include most of my SVG icons that require simple styling, I do:
Update september 2018: this solution is deprecated, read Jon’s answer instead.
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React doesn’t support all SVG tags as you say, there is a list of supported tags here. They are working on wider support, f.ex in this ticket.
A common workaround is to inject HTML instead for non-supported tags, f.ex:
render: function() {
var useTag = '';
return ;
}