That looks like a White Carrara Marble.

Beautiful bathroom!

The floor is 12"x12" Italian Carrara marble in honed finish.
So, as the vanity top.

The shower walls are 3"x6" Calacatta Oro marble from Italy, in the honed finish as well.

Will this marble make the floor slippery? I've been advised to stay away from marble for this reason. Thanks!

No, any surface with Honed/Matt finish should be fine.
I grew up on a polished Crema Marfil floor at my parents house, me and my brother use to fight all the time, maybe we crashed our heads few times, but we survived.

In general when people talking about slipperiness, usually it is when the surface come in contact with water, that what makes it slippery.

When we speak about porcelain tile, most of the porcelain tile will pass the nonslip code, even if they feel a little slippery.
In the process of making porcelain tile, they would add another ingredients to the porcelain mix, that when it comes in contact with water, it will not be slippery.