Why do many economists believe that money is neutral in the long run? If a central bank carried out monetary policy that consisted of multiplying each person's wealth by a common factor, I would find it plausible that all prices would get multiplied by the same factor and there would be approximately no real effects.

However, this is not how central banks carry out monetary policy. They print money and engage in market transactions that target certain prices. To me it does not seem plausible that this has no real effects, in the long run or the short run. 

My question is, why do many economists believe that money is neutral in the long run? Do they take the quantity theory of money as proof that money is neutral in the long run? Is there particular empirical evidence, or influential papers that have convinced many economists that money is neutral in the long run?
There are multiple ways that a central bank can resort to apply its designated monetary policy. The most common one is called "open market operations (omo)", which is basically selling/buying government securities to/from private individuals or organizations. Through these operations, central bank affects the level of cash reserves in the banking system since it deposits/withdraws payments for these government securities to/from the banking system. When cash reserves in the banks go up -by central bank buying government securities-, these banks decrease their interest rate to deplete the extra added cash reserves, and the vice-versa.

As you can see, in this mechanism the only price that is changed "directly" by central bank is the price of government securities. Once the cash reserves in the banking system reaches its targeted level, the probability that the general price level in a specific market will be affected is equal for almost all markets. Thus the operations of central bank does not aim at specific markets, alterations in the interest rates affect the whole economy equally by average.

There are tons of literature, both theoretical and empirical, focusing on the neutrality of money. You can also search them via Google Scholars.