Final Cut Pro supports 3GP, AVI, MP4, MXF, QuickTime, AVCHD, DV, DVCPRO HD, H.264, HDV, Motion JPEG, MPEG IMX format, so i think you can convert files from mts to some other format like mp4, avi, etc.
see: https://www.ilikemall.com/how-to/convert-mts-to-mp4-mac.html
It works fine for me.