We have a new tankless water heater. We hoped this would solve our problem, but still getting dirt in hot water in the tubs.

only the tubs?

Where is it happening, how long, where is your water from? public, rural, well?
In the well systems around here it is not uncommon, and an old hot water tank will actually stop some of the mud from showing up for a while(because it takes a bit to accumulate in the tank) If you aren't on well water, what is your water pressure at the moment when you test it with a pressure gauge.

We are on well water. We have new hot water heater and culligane filtration system. It only happens in tubs. The house was empty for a few years but we have been running water for 2 months. Could it be in pipes?

Yes, only in tubs. We have well water.

if the installing plumber used steel nipples to attach the tub spouts, that will cause a short burst of rusty water when you turn on the tub/s.

I suspect that you only see the dirt in the tubs because the concentration is too low to be spotted elsewhere, and bathtubs allow the dirt to settle out of the water. If you are getting an ounce of dirt per 100 gallons, spotting it in 32oz of water is going to be nigh impossible, but 25 gallons in the bathtub? Much more likely. Your pipes are probably full of dirt in all the horizontal lengths, and the bottom of your hot water heater as well. There isn't a good solution to stop this; a whole house filtration system doesn't help as much as you would like. A truly good filtration system would plug up immediately, and the filter changed almost daily. The culligan filter may not be working, but without replacing all the old piping that is full of mud from years of use, there is no way to tell. I repiped a ranch style farmhouse a few years back, and there was about 1/4 inch of mud in the horizontal runs from one end of the house to the other. Short of repiping your house, there isn't a lot that can be done. Keep in mind, a little mud never hurt anyone.