There are some credible studies now that strongly suggest that the MMR vaccine "primes" the immune system to fight against COVID. In this paper:
COVID-19 has presented various paradoxes that, if understood better, may provide clues to controlling the pandemic, even before a COVID-19 vaccine is widely available. First, young children are largely spared from severe disease. Second, numerous ...
mbio.asm.org
the researchers indicate that the protection provided from the MMR vaccine is likely coming from the mumps portion, as the severity of symptoms was inversely proportional to the amount of mumps titer in the body. They looked at a selection of known (through lab tests) COVID survivors and selected those young enough to have received the MMRII (second gen) vaccine that was given starting in 1979. Compared them with folks over 57 who had received basically no MMR vaccine and found striking differences. (It didn't come into play in combination until 1971). Like the TB vaccine, they lean towards thinking that this could explain why the disease is far more devastating in the older population than the younger.
When I thought about it, it made sense to me to get that vaccine for two reasons. One - the possibility that this could confer some immunity while I (at 77) wait for the COVID vaccine to come my way. Secondly, I live in California where there is an active anti-vaxxer movement and thus kids now getting infected with measles who could pass that along to me. Protection against measles is a pretty sure thing. Protection against COVID is a strong possibility. We'll see....