The rainy forecast for Trump Inauguration will reduce the number of people who attend because the reality is that people don't want to stand around in poor weather conditions to watch many events, let alone one where they might be 1000 yards away. As I say, let it rain, let it rain let it rain.
Unless the weather were to be extremely severe, it is unlikely that it would reduce turnout for the Presidential Inauguration. In this particular case turnout should be high, as both pro and anti Trump people will most likely attend. As Trump has had so much publicity focused on him, both good and bad, this should prove beneficial in increasing the number of people who show up.
There are not very many tickets available for the inauguration. The people who have them are some of the most enthusiastic people about politics. They are excited to see Trump's inauguration. They are not going to let a little bit of rain stop them, even if umbrellas are not allowed.
The number of people who show up doesn't depend on the weather, it depends on who can stand him and who can't. I think there will be a considerable crowd but not everyone is going to be his supporter. I hope the protesters protest peacefully and that there is no violence. This is a democracy after all.