Is Facebook's Libra a threat to the U.S. dollar as a reserve currency? I've heard that Libra would diminish the need to hold U.S. dollars and thus diminish the power of the U.S. dollar as less people would hold it to secure their transactions. Is this true?
In the short term: No.
The Libra website says this:
What are the actual assets that will be backing each Libra coin? The actual assets will be a collection of low-volatility assets, including bank deposits and government securities in currencies from stable and reputable central banks. [...]
So the Libra depends on the dollar (and other reserve currencies) in order to retain its value. It will not displace the dollar unless it eliminates dollar-backed assets from its reserve. This is unlikely, as US Treasury securities are widely regarded as some of the safest investments on the planet. They are a necessary part of any scheme even vaguely similar to what Libra describes.
In the long term: Probably not, but the dollar's days could be numbered regardless.
Unless Facebook or the Libra Association make dramatic changes to the structure of Libra, it will never be a "true" reserve currency. It may become more convenient than reserve currencies, and regular consumers may choose to use it as if it were a reserve currency, but most major governments and large NGOs will likely prefer to manage their own baskets of foreign assets directly. As discussed below, governments in particular have had the option of using special drawing rights as a reserve for as long as modern fiat money has existed, but they have largely ignored this possibility, preferring the dollar and other "stable" fiat currencies. There is no reason to believe they would treat the Libra any differently.
However, there are reasons to be skeptical of the dollar's long-term dominance. It is controlled by a single country, with a mercurial and idiosyncratic fiscal policy. The Federal Reserve is primarily concerned with the well-being of the US economy, and not with the dollar's continued suitability as a reserve currency. These interests are related and usually aligned, but it is not inconceivable that a domestic financial crisis could motivate the Fed to engage in monetary policy which is contrary to the interests of foreign governments. On the other hand, it is possible that the Euro or another non-US currency could be more widely adopted as a reserve currency, although the ongoing sovereign debt crisis in the Eurozone makes this unlikely in the near future.
Baskets of currencies are already a thing, and have been for a long time.
The concept of using a basket of foreign securities in lieu of an individual reserve currency is not a new idea. Special drawing rights are a financial instrument administered by the IMF in a similar manner to Libra, but they are far older, having been established under the Bretton Woods system to simplify the then-common practice of pegging the exchange rates of various world currencies to one another. SDRs cannot be purchased or held by private citizens, however, and have therefore fallen into relative disuse in developed countries now that Bretton Woods is defunct. So Libra might well fill a gap by making itself available to the general public. But that would not make it a "reserve currency."
One problem with the SDR that has hindered its adoption as a reserve currency is its relative lack of liquidity. To overcome this problem, Libra would need to be much more liquid than the SDR, which would involve creating a very large volume of Libra. For reference, the IMF has allocated more than 200 billion SDRs, with each worth 1.38 USD at the time of writing, and this is regarded as far too small for use as a reserve currency. But to issue such a large volume of Libra, the Libra Association would need to control and manage a very large volume of assets to back the Libra. I suppose anything is possible, but it strains credulity that world governments would voluntarily give that much power to a private organization absent some compelling need. It would be far easier to just persuade the IMF to issue more SDRs.