Is there no way to do this? For example, if you're in behavior > all pages and want to see the current month, you have to change the ending date to the current day every day.
1) Go to the right upper corner.
2) Click on 3 vertical circles next to your gmail icon
3) You should be in "Edit User Settings". Change default date range to 30 days.
4) Hit "Save User Settings"
You should now see 30 day stats under your GA account. Including behavior stats and whatnot.
It's not exactly "current month" settings, but last 30 days. If you want to see just April and today is April 10th, then you should select April days and always do it manually. Sorry, GA doesn't have that.