That's what I was hoping for! A quick coat of poly just to keep it sealed.

You can use MDF, and you can put some wipe-on poly on it for some protection, but I think there are better products out there for shelving. If you do use MDF I would make sure anything you put on the shelf is dry. Poly won't protect MDF against water like a full paint job would. If nothing wet will ever touch the shelf, it's probably not a big deal.

MDF isn't really wood in the traditional sense - it's compressed sawdust and glue. It's very flat when structurally supported, but it's also very heavy and can definitely can sag if not supported, depending on the width of the shelf and the weight placed on it. It also doesn't accept screws very well near the edges where splitting is an issue. If the shelf span is wide and it's sitting on a normal shelf pin system, only supported on the sides, I could see sagging being an issue over time if the load is enough. So it might depend on your use case.

My question is, if you like white, why not use melamine? And if you like natural wood look, why not birch plywood? Those are kind of the two default materials for cabinet carcasses and shelves.

There are also MDF cores that are veneered with wood for more of a traditional wood grain look, and it would offer that extra surface protection against moisture if properly finished. Would probably need to be edge banded in the front, though.

@Nick Miller, sure wish I'd read your comment before our custom closet maker talked us into raw MDF shelving (with Baltic birch and poplar trims and support, thankfully). We now have a ton of it in five rooms and are trying to figure out how to seal it before moving our stuff in. Ugh.

@Mittens Cat, do you need to seal it? If you don't mind the look as-is and they aren't kitchen or bathroom cabinets that might see moisture, then you probably don't need to do anything. MDF does expand and contract a small amount with big temperature and humidity swings, but nothing you'll notice. Other than that it's quite stable and not prone to warping or cracking or anything like hardwoods can be. You can put a polyurethane coating on it, but MDF is very absorbent and really soaks up the finish so it doesn't leave much of a protective layer. It does leave it a bit darker in color, though. But definitely wouldn't protect from standing water at all. I wouldn't use the material in a kitchen or bathroom, but if they are bedroom closets or general storage for dry goods, I'd probably just leave them raw. I don't think any harm should come of that and it seems like a lot of work for minimal protection.

One thing you might want to do if it hasn't been done by your carpenter already is gently hand sand the edge of the shelf fronts. Just to knock back the sharpness. It will help reduce the chance of splitting or denting the edge as you take things in and out of the closet.