Will a worn out water softener make silt in my bathtub and toilet bowl

Must be on a well.

Must be on a well.

Yes it is on a 23 year old well 120' deep. Water softener is also 23 years old, never had a silt problem until 3 weeks ago

Don't think softener will be source of silt. If you are finding it in bathtub must be pretty bad.
First I would flush pressure tank. May be an accumulation there.
If it persist you will probably have to install filters or sand trap or both.

Don't think softener will be source of silt. If you are finding it in bathtub must be pretty bad.
First I would flush pressure tank. May be an accumulation there.
If it persist you will probably have to install filters or sand trap or both.
I replaced the pressure tank yesterday, old tank had very little silt in it

Have you been dry for a long period and the water table be droping?

Have you been dry for a long period and the water table be droping?

We have had the dryest year here since 1911. I thought of that possability also but I don't use a lot of water, possibly 100 gallons a week. Would that much usage bring my water table down enough to cause this problem?

Not what you use. More about the lack of rain in that area and what other people are using.
If you are using only 100 a week that might be part of the problem. Open a faucet and let it run for a couple days to see it that clears things up.

Sure sounds like the water table has fallen and the well is closing in allowing you to pump silt, Harold advises,
Open a faucet and let it run for a couple days to see it that clears things It's not often I disagree with Harold but I'm afraid if you do that you'll just lower the water table farther and make a bad situation worse. I would call in a well company and have the well checked out, You might have to go deeper. Good luck, Tom