Flush mount sinks

Is it okay to use a flush mount sink with a solid granite countertop?
The granite installer is afraid water will seep between the granite and the sink and rot the cabinets. Do they make a moisture bearer that we can lay down that will work with granite?

Listen to your granite installer. Undermount works best. And they look good as well.

Any kind of sink is appropriate....drop in, rim mount, or undermount. Undermount would be the preferred with granite. No matter what the countertop material is, the sink should and can be installed so water does not leak under.

Does changing from an overmount sink to an undermount sink affect re-attaching the drain pipe? New sink is 1" deeper, plus lower placement.

Silicone!!!

If you go with an undermount (my preference), it is likely to cost you a fair amount of money. The cutout of the counter if prepared for a drop-in sink will not be the same as it would be for an undermount. It might end up costing huge money to cut and polish it. WHen they do it in the shop, it cost me $350 for the sink cutout with polished edges - a hole for a drop-in won't be polished and may be shaped differently than an undermount. After the fact, it could be really messy and you might need to just throw away the slab and start over.

You need to be careful as some silicon combined with some stone can stain, but they should be able to recommend one that will work in your situation. I wouldn't be worried about water leaking and ruining the cabinets...how often do you have a lot of water on top of the counter? You'd want a tray if you air dried dishes, but other than that, it would be a rarity to have liquids there.

I find it much nicer without the lip on the sink. It is much easier to brush crumbs and crud into the sink when it doesn't have a lip.

What do you mean by "flush mount"? That would usually describe a sink with a metal rim around it. Sealing a "drop in" sink is EXACTLY the same as sealing an undermount one, in fact easier because you do not have to worry about the sink being filled with water above the caulked seam.