Stu is absolutely correct w/r stretch. The 'best' (so far) in synthetics is Dyneema but it has ~3 times the elasticity of simple 1X19 wire. What would mean for standing rigging that the top of the mast will move/oscilate 3 times as much as with 1x19. eg.: StaSet-X has 15 times the 'stretch' of 1x19 wire.
Standing Rigging isnt ONLY to 'hold the mast up' ... with respect to the forestay/headstay its also responsible for SAIL SHAPE of the foresails. ALL headsails are especially cut/designed so that the sag of the fore/headstay under sail induced loads MATCHES the expected sag of the rigging/forestay; they are cut with a smooth curve at the luff to compensate for this expected and predictable forestay 'sag'. Since the best of exotic synthetics have three times the elongation under stress than 'wire' you will have to compensate by increased (3X) backstay, etc. tension to get the 'designed' sail shape ..... and the message here is that ***your chain plate attachment system may not be strong enough to support such additional loads*** !!!!!!!! So, if you put up synthetic standing rigging, including the fore/headstay, you will have include the cost of recutting the luff shape of all your jibs/genoas ... or if you dont you can expect very degraded performance (especially ability to 'point') from your headsails.
Dyneema and other exotics are also subject to 'creep' ... permanent elongation under constant stress .... so you will have to constantly 'chase' the tension values as the synthetic progresively changes length. Not a problem for use on running backstays, backstays with ample adjusters, etc.; but especially for the 'set and forget' wires, if you dont 'keep up' with the length changes, you will be experiencing 'looser and looser' rigging.
Presently the use of 'furlers' in which there is a lot of foil and drum contact with the wire rope would create bodaceous 'chafe' points on a synthetic ... and most synthetics cant handle 'chafe' and abrasion very well, at least not to the ability of wire.