FR-4 is a flame rating- how well the material can burn. It has nothing to do with it's electrical, and even mechanical properties. It is highly unfortunate that the FR-4 name has "stuck" as a defacto standard for PCB laminate names, but that is the world we live in...
Even when specified further as IPC 4101\21, that standard lists FR-4 material as maximum permittivity to 5.4. What that is means is that many/most (?) compositions of epoxy/glass fibers (and dimensions of the glass fibers!) that gives the ratings listed in the IPC standard can be used. It is perhaps slightly better than just saying "FR-4" but I would belive that any "FR-4" materials on the marked are in accordance to IPC 4101\21, as I belive the FR-4 term originates from that standard.
If you want repeatability for FR-4 boards you should contact your fabricator, agree with them on a specific material vendor and then specify that - if they will let you. (rembemer; permittivity isn't a controlled property for FR-4, so manufactures are not monitoring that in the production line. Why should they? That would just add cost. So likely they are not able to give a statement saying that "our material has Er of 4.4 +/-10%).
So: If your design has critical requirements for permittivity (I.e; that your design cannot tolerate variations, and/or has frequencies of several GHz and above) you should use materials where a specific permittivity is listed in the datasheet. FR-4 is not the right material for you. Again, contact your fabricator, they will have several options.