How many inputs can a single mcu output drive?
Some important specs I got from the Attiny datasheet sectiosn 21.1 an 21.2 is that dc current per i/o pin is 40mA. Only a few pins can operate at this limit at any given time, check out the electrical characteristics its very useful.

Just for fun, let's say every device you want to drive is another attiny, from the datasheet we see maximum input leakage (low or high) is 1uA. So exceeding the 40mA per pin would be highly unlikely. As other said the real concern is how LC losses for high freqeuency signals.