Double sided tapes are very widely used in the framing trade, but should never come into direct contact with artwork. The one exception to this rule is that Needlework tape has been designed specifically for attaching embroideries to a backing board. Using Needlework tape to frame art on fabric is much quicker and easier than the tradional 'lacing' method.
One of the main uses for double sided tape in framing is in making double mounts. ATG (Adhesive Transfer) tapes are very quick and easy to use for this, although the applicator guns can be rather fiddly to load at first. This does become easier with practice. For conservation mounting, consider the Acid Free ph7-70 ATG tape.
For lower volumes, fingerlift tapes work very well. 'Fingerlift' simply means that the peel off backing is wider than the adhesive, making it easier to remove quickly.