Will depend on your city code. I live in San Antonio Texas and the city code required 2" for a double drain system

to be precise about it, the answer will come after you re-specify whether you meant 1.5" before the P trap or after the P trap, and whether you meant the two drains are combined onto one P trap or not and so on. These different pipe segments may be governed by different rules, which do vary from place to place. In general you are right that 1.5" is OK and that it is safe to hook up a double bathroom sink to a 1-1/2" drain, and so the most likely answer is no to the one guy who wanted a 2" drain. BUT there may be other things you need to tell us. Ask the 2" drain plumber what made him specify 2".

It would depend upon which code they are under.

A lavatory is rated at 1dfu.

Under the IRC an 1-1/2" horizontal line is rated for a maximum load of 3 dfu's.

Under the UPC an 1-1/2" line is rated for a maximum of 1 dfu, which would be one lavatory. Adding a second lavatory would make the combined load 2dfu's and it would require a 2" line.

Under UPC two lavatories could be combined into one common trap connected to an 1-1/2" line provided the horizontal center to center distance between the two lavatory drain openings does not exceed 30"

I am assuming you have a vertical pipe in the wall, and will have an 1 1/2" sanitary cross cut in. In this case you should be fine as long as the piping is vertical at the tie in. UPC allows two fixture units on 1 1/2" when vertical.

Good Luck

Here is a link that might be useful: Universal Plumbing Code PDF

UPC is Uniform Plumbing Code, NOT Universal.

IRC is International Plumbing Code.

They are the two most common model codes in the US, often adopted with at least some state or local alterations.

Call your AHJ (Authority Having Jurisdiction, the inspectors) to find out what code you are under, and any local alterations.
We have had a long history in the US of competing code making authorities.

The more removed from doing actual plumbing work the code writing folks are the worse the codes seem to become.