EyeTV has been running on my Macs since 2002, literally every second my Mac is on. Currently it's working fine under Sierra betas. At the same time I might be running Photoshop filters, demanding games, QuarkXPress, inDesign and Illustrator, etc. EyeTV has never interfered.
It has run on my various Powerbooks, G3s, G4s, G5s, MacPros and iMacs. The Elgato 410 Firewire tuner even runs along a FW network and is currently connected to a Thunderbolt port on a new iMac. Otherwise, wireless network connections make it easy to watch EyeTV on iPhones and iPads and also any recording made by EyeTV. The Elgato Turbo 264HD compressor sticks are not necessary on modern Macs but are good on slower ones and also mean you can compress or convert two movies at a time.
The Elgato 410 has proven to be the best of their tuners in my area which has patchy TV reception. I have four other tuners from when I did a head to head test for a magazine.
I read some of the comments below and am persuaded they are linked to the individual's Mac rather than EyeTV itself. I have had occasional glitches with the software but they are easy to fix, usually by completely uninstalling EyeTV and starting again, a matter of a few minutes at most. There are various guides to do this on the web and Elgato's site which also has free tools to help.