I am wary of sidechains because of the mining incentive issue. Moving transactions off-chain leaves miners underfunded in the far future, or else results in very high tx fees, leaving Bitcoin more open to competition from a more inflationary coin that pays miners through block rewards more and tx fees less.
However, on that note I have to admit there is little substantive difference between sufficiently high tx fees and slightly breaking the 21M coin limit (no halving, or slower halving), since you can't actually benefit from your Bitcoin wealth unless you spend it eventually, at which time if you incur a big tx fee as a tax it is no different to you than an inflation tax. OK, maybe certain people will gain/lose more from high tx fees vs. inflation. Nevertheless, one way or another the miners have to get paid, and if Bitcoin is severely under-mined due to SC then one of those two things will eventually happen, or else Bitcoin (the platform) will die. But I think Bitcoin the platform will only be allowed to die if everyone is confident that Bitcoin the ledger will live on in an even more secure form as a sidechain, spin-off, or something else. So I'm not so worried about sidechains from that angle, since in such a case the investors lose nothing. And if such confidence can never be gained in the first place, sidechains will never reach such a threat level.
If you are currently a holder of 1% of "the ledger currently being updated by Bitcoin," and at the end of the day your private keys still control 1% of what is now the ledger of civilization, you haven't lost any purchasing power, provided whatever protocol is updating that ledger now is at least as secure as Bitcoin. So I see no danger from perfect sidechains (sidechains where the 2wp is permanent and the sidechain never fails and can somehow live on its own if Bitcoin-the-platform dies) although a very successful one could force Bitcoin to choose between high tx fees and some continuing inflation, but I see a possible threat from imperfect sidechains (2wp is broken and/or mining incentives get messed with) though it seems somewhat self-limiting in that most investors would be tentative about moving their wealth until the peg is proven to be as strong as Bitcoin itself.
In some sense if you're worried about the economic majority just being dumb and moving to a doomed sidechain because of naivety, why not also worry about the economic majority supporting some really bad change to Bitcoin that kills it? The nature of Bitcoin is, in part, that we trust the economic majority to have a certain level of sanity.
In summary, investors shouldn't be wedded to the protocol per se, but of course to the ledger and their percentage stake in it. If there is a better protocol for updating that ledger, and it can be proven to my satisfaction that it is superior (an extremely high bar), then I say bring it on, since it just means the ledger and all investment stakes in it become even more secure (ex hypothesi; again, if there is any doubt of this then I for one won't be excited about it, but I think - for the same reason - most others won't either).