Being away from Tumblr/Twt for a while, I'm very confused on what "DNI" even means. Do I have to check the bios of every single person while scrolling before hitting the like button? Or it's just for communication? Is it safe to like from an account without the specific warning?
To start, DNI means "Do Not Interact"
it's a list of people who the OP doesn't like, such as people who are bigoted, but it can be as specific as people who ship a fictional pairing or have a specific aesthetic they enjoy.
Certainly, it may be more important to the person with the DNI if you're having a direct conversation with them, out of fear of you "corrupting" them by chatting. Some may even think you're "tainting" their posts by putting it on your blog or liking it. It's a highly contextual and social thing, so the best way to answer is "depends on the person with the DNI".
As for the last question, I'm not sure what the angle is there.
If you mean if you want to like a post you would use a blog that doesn't allude to anything on the DNI, well, do that if you like. They don't know you!
If you mean trying to fish for a version of a post without the user's DNI on it, I think that's fair to a point, because if you want to reblog a huuuge thread with several people who may have a DNI, it's a lost cause. The human brain can't work with that many layers, and my personal opinion is that the effort of being avoided should be absolved by the person with the DNI. Though, if you mean trying to just reblog from someone who doesn't have a DNI, even I do that! No one even looks at who you reblog from most of the time, and if you just want to avoid being in their notes, that's the best option.