Can I safely order these chips for use in a (Bluetooth master) 3V3 <=> 5V (ATtiny) level shifter application? And how can I conclude that from the datasheets?
For unidirectional data flow, although there will be shifters more suited to lower voltages, you should be fine with this chip. On page 6 of the ST datasheet, there is a High voltage vs Low Voltage graph which indicates a minimum combination of ~3V for Vcc and 5V for Vdd:
If you are using both Rx and Tx, then you will need a bidirectional level shifter, such as the ADG3304. Or you can use two unidirectional ICs, as discussed in the comments.