That tape looks to be getting a bit shabby. I think I'll use some of my black stuff along that area.
Yes. I replaced that tape asap on our Jaycos.
Unfortunately, many manufacturers use it. That tape, however, and the manufacturers' installation of it are
not examples of high quality material and workmanship. A lot of owners have had issues with it wrinkling and degrading. Once the deterioration and/or wrinkling begins, water penetration under the tape is inevitable.
After that, as the water "pools" under the cheap tape, the screws begin to rust and corrode, and the water makes it's way into the slideout roof decking, insulation, and framing. If left unaddressed, the water will eventually damage the ceiling board. It's definitely well worth the effort to address it sooner than later.
4" Eternabond tape with sealant-beaded edges is an excellent, long-lasting upgrade. Eternabond caulk or XTRM Ply 100 (by LaSalle Bristol) work well on the tape edges. You can apply a 1/4-1/2" bead along the edges. The XTRM Ply 100 comes in a self-leveling formula, too. When I use the Eternabond caulk (or any non-leveling sealant), I smooth it a little with a mildly soapy finger (usually diluted Dawn).
To ensure excellent adhesion and longevity, it's important to prep the roof surface with a cleaner and a primer. For me, the cans of Eternabond cleaner and primer are the easiest and cleanest method to get it done. You can use mineral spirits for the cleaner, but I would not skip the primer. It's a light glue aerosol that provides a little tack for the tape to bond with.