Final Cut Pro X
FCPX can work with .mts natively.
Supported media formats
You can import and work with the following video, audio, and still-image formats in Final Cut Pro:
Video formats
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Source: Final Cut Pro X Help: Supported media formats
VLC Nightly
The latest nightly build of VLC seems to be able to play some .mts files — others just freeze.
VidConvert
For other cases, I convert them to .mov using VidConvert.