No grafting tape for me. I learned to graft with Parafilm M and grafting/budding rubbers - but switched over to office-store rubber bands, when my supplier of grafting rubbers went out of business. I had one bag of rubber bands, from Wal-Mart, that would photo-degrade and be peeling off within just 2 or 3 days, so I started doing a wrap of a couple of layers of masking tape around my graft unions before overwrapping with rubbers, just in case they break down too quickly.
I graft a lot of oaks, pecans & hickories... they take longer to callus in and commence growth than do apples/pears/persimmons, etc., and need longer-lasting 'wraps', hence the use of a more long-lasting wrap such as rubberized electrician's splicing tape or duct tape.
I tried Parafilm Grafting Tape once... but for my purposes, it was vastly inferior to good old Parafilm M.
For small stuff, where I'm doing a whip & tongue, cleft, or simple bark graft, I'll wrap union and scion with Parafilm, then overwrap the union with a layer or two of masking tape. Then, overwrap that with a #64 rubber band.
If I'm doing a TX bark inlay type of graft on a big rootstock (like the persimmon in the photo), I'm going to wrap with rubberized electricians splicing tape or duct tape, then cover the graft unions and exposed top of the rootstock with aluminum foil. Then, later in the season, I'll come back and remove the foil and cut the tape so that it can fall off rather than potentially girdle.
If you're going to be grafting pears or apples... you don't need much. One of my friends and orcharding mentors ran a noted fruit tree nursery (Rocky Meadow) in Indiana for many years... Almost all of his apples & pears were grafted with a whip & tongue, and the graft union wrapped with nothing other than masking tape.