Completely freaked myself out by cutting my nails (ok, that sounds super weird!). Been doing Josh lessons for about a year. I have fairly long nails (in comparison to other bass players). I clip them every once in a while but I am not super conscious of it. The other day I clipped them and then WOW - this horrible sound resulted. I literally looked at my bass because it was so terrible. I kept cutting and cutting and nothing really helped and my finger tips were not happy with me. I walked away came back the next day. I adjusted my fingers to try to keep the meat on the string. And I got better and better at it. But the tone is completely different. I kind of miss that clack a little bit and my fingers feel really different on the string. So really? Just cutting my fingers threw my whole pluck and playing into disarray??? I did a bit of internet reading and it seems like nail length might be a preference? As I am waiting for my fingernails to grow a bit as an experiment - what does everyone think? Am I imagining this? Am I overreacting? Is it one of those things that I didn’t “hear” until I cut them a little lower than normal maybe? How can I be so mystified?
My guess is you learned plucking with your fingers the “wrong way”, such that you hit the strings with your nails a lot/all the time!?!
The “textbook” way would be using more of the fleshy part of the finger tips, and for that it is often better to keep the fingernails short in order to have a more consistent tone.
That all said, there are players who use their fingernails like a pick/plectrum in order to get a more distinct attack (the “clack” you mention). However, I would assume even these players only use it sometimes, and other times, they pluck with the fleshy part.
At the end of the day, it is a personal decision on what kind of tone you like. But also be aware, that different types of music might require different ways to “attack” the strings; or, if not require, then at least work better with a certain tone.
Perhaps you might want to experiment playing with a pick. It is a different feel, for sure, but it should give you that clack you are missing 
This is great.
The first time I changed my strings on my bass - after 2 years of serious abuse and use… I hated it. I swore I’d never change strings again.
My bass had been this thuddy, dead, chunky thing and then it became this super chimey, bright, treble-y instrument.
I think that our ears get very used to whatever it is we expose them to.
The more we hear it, the more we internalize it as good and safe and happy.
So, as someone who now loves and cherishes the sound of new strings - I think you’re just going to go through a weird patch of ear re-adjustment.
If it’s monstrously terrible, send us a video clip of the no-nails finger style and maybe I can offer something more specific… but it sounds like the horror of sudden change to me - something that I can definitely remember and relate to.
Plucking using nails for classical guitar is a time-honored technique. Trying the same with steel string guitar requires a light touch and a whole lot of nail maintenance to achieve consistent tone and attack.
Using nails on a bass (either partially or full-on) is also a thing, but it is usually used only intermittently, many times for emphasis.
Joerg is likely right on: You became accustomed to your nail-sound as you played.
While your nails grow out, take this opportunity to learn/practice how plucking with your fingertips sounds. It’s worth it in the long run whether you go back to nails, or not. Hang in there.
Well I will tell you that I have tried to play with a pick a few times trying to get the sound of a Thin Lizzy song and WOW was I terrible. I had ZERO control. I know it just takes practice but I was surprised at how uncoordinated I was. 
I think I just turned myself into a one horse pony and I need to think more diversely. Thank you for the great comments.
Thank you. I have adjusted pretty well over the last couple of days and only hit my nails every once in a while. I just had no idea that so many different sounds could be created! I thought I had ruined my playing forever (yeah, I am an over-reacter!!) So though I initially panicked, I am learning there are different ways to “pluck”. Thanks for the encouragement!
As with the others, I think you are spot-on. I just was used to my sound of things. I also have never changed my strings - and my boyfriend changes his routinely. He LOVES new strings. Thanks for making me feel a bit less crazy. I stayed up WAY too late that night trying to figure out what was happening! ha ha ha
Personally, I keep my nails short all the time. I don’t really like the extra clicky sounds that come with long nails. It’s also to prevent incidental contact with strings I’m not playing. I think most bass players keep their nails short for those reasons, but at the end of the day it’s really a matter of personal preference. Geddy Lee always kept at least one of his plucking nails long so he could attack the strings and get a pick type sound when he wanted to.
If you really dislike the sound, then just grow them back out. It shouldn’t affect how you play though. Your fingers should contact the strings in basically the same place whether you have nails or not.
In my experience, it’s much more difficult to play cleanly with the fleshy part of the fingertips if you have longish nails. The longer, the more difficult. It’s just not worth the effort of trying to get around it.
It sounds like the OP is having success exploring many sounds with shorter nails. All the best with that.