How many will listen to tape and vinyl in the next century?

After 100 years the main problem will be to find high quality original pressings. Most reissues are average sounding and they may not be able to carry the game of analog forward. We need seriously good sounding vinyls in plenty numbers in order to keep the interest going. 

Even today if we had to live off only the reissues a lot of us would lose interest in analog playback IMO

There is still a lot of good original pressings around from 50s, 60s and 70s. Many of them held up remarkably well, but I don't know about 100 years more,  enough of them will probably deteriorate. In a hundred years playing records let alone tapes, if there are any tapes, may become sort of a strange elite, even aristocratic, hobby. Better than nothing.

And thats the worry, the shortage of good LPs.

Tonykay, right about Willy. Six years ago he aligned and calibrated my 682ZX extermely well. Going to send the deck to him this year again to have it in perfect order for the next five-seven years.
As for the next century..well, someone got to replace him. And us.
I do sound optimistic, don't I?