Steps to Reproduce:
@chrmarti I'm assuming you're using the dark theme. I tried on Windows 10 and the I is rendered by Windows in white. Maybe it does have something to do with your setup? Do you see the Windows cursor or the OSX cursor?
I'm using the default Dark+. The cursor seems to be from Windows (no extra horizontal line in the middle). It's Windows 8.1, but nothing else I'm aware of that would make the setup special. Also the hand and the arrow cursors both are white with a black outline (as expected I think).
This is how it looks for me:

Here are my cursor pointer settings:

I am on Windows 10. How does the cursor look like for you if you visit https://code.visualstudio.com/ and hover over the copyright text at the bottom in Chrome?

Indeed, the cursor shows the same behavior (black on black text selection cursor) on the code.visualstudio.com website.
@chrmarti In this case, please file a bug against Chromium (or if the black on black text selection is reproducible in IE against Windows)
Appears to be a known issue with Remote Desktop for OSX. Older versions reportedly did not have this. The discussion linked below suggests to swap out the text selection pointer with "beam_r.cur", that works for me.
(https://social.technet.microsoft.com/Forums/windowsserver/en-US/cf05826e-63a4-49d9-b812-7a4695832ab8/rdc-mac-version-8024091-can-not-see-cursor-in-any-editor-with-black-background-because-it-is?forum=winRDc)
@chrmarti Nice!
@alexandrudima Thanks for helping track this down!
Most helpful comment
Appears to be a known issue with Remote Desktop for OSX. Older versions reportedly did not have this. The discussion linked below suggests to swap out the text selection pointer with "beam_r.cur", that works for me.
(https://social.technet.microsoft.com/Forums/windowsserver/en-US/cf05826e-63a4-49d9-b812-7a4695832ab8/rdc-mac-version-8024091-can-not-see-cursor-in-any-editor-with-black-background-because-it-is?forum=winRDc)