I've lived through 2 house remodels. Yes, take out the bathroom tile NOW and live with the concrete boards. It's not that bad. really, it isn't. Take your time and go through magazines and pull out the pages that you like and put in a folder.
While your contractor is there and doing all the other work, have him do this too. Otherwise, you'll have to go through the whole process of calling him or someone else to come back. It will cost you more.

Are the concrete boards what is already there under the tile, or is the contractor putting down new concrete boards after he rips out the tile? Are you planning on making any footprint changes in the bathroom at any point, or just eventually switching out the tile? Because if you are planning any big changes in the bath, you might want to wait to do it all at one time. Otherwise, if the concrete boards are to be newly installed, you're paying for an interim concrete board finish that will have to be ripped out again anyway.

We are not planning to change the footprint. We'd like to change the vanity and the tile. There are concrete boards under the tile, but he said he would put down new? I did not know about the finish - interesting. Thank you