I get this problem. If I have a weapon in my hands and I use the hot keys to change to a different weapon no problem, the character keeps running. However if I have no weapon or item in my hands and I use the hot keys to equip a weapon into my hands then my character will stop until the animation is completed, usually followed by "you are dead or unconscious"

Don't think it's a bad thing that you can't run while changing weapons. Not stopping though, just walk with normal speed sounds okay to me.

Even holster a pistol full speed running isn't that easy.

Devs already say the new animation system will add the function to perform actions regardless to movements. You should be able soon to wave at someone and walking, or take out a gun while running and stop before animation is done. For now you can't change your speed until take out animation is done, and some actions (take out gun while walking) will stop you.
Wait.

Hello makethemsuffer111 and thank you for the report.
This is an issue we are aware of (#0021789) and it has been scheduled for a fix.
Regards,
Geez