Most televisions will do progressive (non-interlaced) modes just fine. You're still limited to whatever horizontal scanrate range they will accept, though. For a SDTV, this is 15kHz. This means you can only do ~240 imaged lines progressive while you can do ~480 imaged lines interlaced at 60Hz (you get more if you drop the field rate to 50Hz). Some of the modern stuff with lots of digital scalers won't accept progressive video at such low resolutions, but most of those will accept progressive video at higher resolutions (480p, 720p, 768p, 1080p etc.), so you can just use that.
The TV does not control the video timings. The video source controls the timings. The monitor just syncs to them and attempts to display them. As long as the timings are within the acceptable range for the monitor, things will work.
My understanding is that most European televisions will accept 60Hz timings and will also demod NTSC color signals (only relevant for composite and s-video). Many American ANALOG CRT sets will accept 50Hz timings as well as 60Hz but will NOT demod PAL color signals. This means that you often CAN feed them "PAL" via component and get something usable, or you can live with B&W if you have PAL content and only composite or s-video. Many of the modern sets with digital scalers seem permanently stuck in "NTSC" mode where they assume 525 line 60Hz inputs, though.