Restaining rough cedar exterior
You will need to take some of the old and new siding in to the paint store to get it matched. Be sure to ask if they match by eye as this type of match can't be done on a computer.
But if it has been 20 years since the house has been stained you want to think seriously about doing the entire house now as i am sure it could use it.
But with the age, it would be smart to do the whole thing, but it's so expensive!
Computers only get you close - it takes human knowledge and skill to match a color exactly.
I doubt your siding has 20 year old stain. Stains don't last that long. It has turned grey because it is old - that's all. That is what untreated cedar does.
You won't be able to "stain" new cedar to look like this - your painters are correct. I wouldn't even try. If you stain it - it will always look different.
You can install new cedar and wait for it to turn (that could take a number of years) - you could install new and apply a "greying agent" - these make cedar grey faster - or you could prime and paint it all.
Mr. Paint
If this is transparent stain or semil solid a computer cannot read a stain unless it is a solid stain because the eye will read right thru to a solid color which would be the wood.So what you need to do is get a higher estimate for your insurance company,you do not need 3 estimates like people think,and is against the law if the ins company makes you.
You could bring in 1 with the most expensive estimate then get a cheaper guy to do it.
I think I'm going to get enough out of them to do a solid stain on the entire house. But if it's grey now, how many coats will it take to do a solid stain in a medium to dark blue?