Please Note that the X-T100 is a very bad camera if you want to use it for streaming as a video capture device.
It does NOT have Clean HDMI out... UNLESS you press the RECORD button, which requires an SD card and is limited to 30min per session... Or you can chose to output 4K to HDMI, bypassing the SD card and the record limit, but that will only be at 15 frames per second. This defeats the point of Clean HDMI out, as the only way you can get it, is if the camera is recording.
That being said, the camera outputs an HDMI source always when a cable is connected, so I don't think it is any settings in the camera, most probably it is your Capture card or the way you set it up on your pc, or your cable...
Try this:
Press: MENU/OK Button
Go to Camera 5 menu
Select Movie Set-Up
Set the following:
MOVIE MODE = 1080 (any frame rate or just set 59.94)
HDMI OUTPUT INFO DISPLAY = OFF
4K MOVIE OUTPUT = HDMI (if Movie mode is set to HDMI)
HDMI REC CONTROL = ON (You probably won't need this, but just in case)
if that does not help, here are some Questions:
What Capture Card are you using
What video capture software are you using, OBS or something else.
what OS are you on? Mac/Windows
Which settings did you use to set up your capture card in OBS / other software
If you plug in other source like a Game Console or TVBox in your capture card, do you get a reading