Pulling up fiber board to install new tile flooring
should I cut the fiberboard up to the cabinets as close as possible
and butt the new cement board up to the cut and tile over it (will
that cause issue with the tile over the seam?)

As close as possible is fine,  and even an inch or so will be fine, especially for tiles that large.
The only problem i would try to avoid is having the grout seam fall on, or near, the joint/seam where the cement board meets the particle board
For under the toe kick of the cabinet you can rent a Toe-kick saw that will give you a cut very close the the cabinet.