Good morning,
I have been reading through the previous posts trying to find some straightforward answers.
As like a lot of people I have my white oak hardwood running up to the tile in the bathroom. Ideally I would like to not have a transition piece or t moulding between them if at all possible. The board is parallel to the tile.

Can I leave a gap close to size of the grout and caulk with some sanded caulking? Will that cause issues down the road?
Thanks

You should only have issues if the wood swells due excessive humidity or water damage. Does the hardwood abuts a marble threshold? If so, is there room to undercut it?

I think a gap one half the grout width looks good. The sanded culling should only be a quarter inch deep, so use a foam space to build up the gap.

Sanded caulking should only be a quarter inch thick or it doesn't cure as it should.
Don't fill the entire gap.