My team is super slow, I turn off emcumbrance effecting the speed of the party in settings so it shouldn't be happening in the first place. I though that the setting was bugged and wasn't working but then I sold most of my items and it didn't solve the problem. Also I couldn't find any toggle off/on option for walking in the controls so I must assume by this point that's it's a bug, but who knows how long I would have to wait untill it gets patched out. It makes the game pretty much unplayable since it effects combat too.

Check, if you accidentally activated Linzi's Acrobatic Skill. If it is activated you move with half speed.

No it wasn't activted, also it wasn't half speed but max possible lowest speed.

UPDATE:
I made a new character(which I actually like more so not much was lost) and played couple of hours to the moment when I encountered the bug. Nothing happend so far but when I load save with my old character the bug still remains.

UPDATE; it's not a bug and I'm kind of dumb. It's a weather effect, when it rains the party is simply walking slowly.

I know this topic is really old, but for me, I somehow turned stealth mode on, which is the little eyeball to the right of your party list along the bottom of the screen. When you're in stealth, there is a bit of a dark blueish shade over your characters on the screen. There is also a bug where Tactical Mode can get stuck on, which you can fix by holding Shift + Space for a moment and then pressing Space again to unpause. I think my problem was both at first, then just needing to click the little eye symbol to turn off stealth.