How to lock down WhatsApp permissions? A number of friends are using WhatsApp for communication. So I'm thinking about installing it. However when I read the question about its permissions I'm asking myself if there is a possibility to lock down the permissions.

I'd like to do have a solution where some permissions are always allowed, some are always blocked and some are blocked, but can be enabled on a temporary basis (like a popup menu which asks). Is this somehow possible? Do some custome ROMs have such a feature? If yes, which?
You can try Donkey Guard the Xposed Framework module from which you can manage permission for apps.
DonkeyGuard allows blocking access for any installed application on your phone to the following data separately:

device_id
phone_number
sim_serial_number
subscriber_id
incoming_call_number
outgoing_call_number
gps_and_network_location
impi_impu
cell_info
accounts
accounts_credentials
read_contacts
read_call_log
call_phone
read_calendar
receive_sms
send_sms
receive_mms
send_mms - not implemented in alpha
record_audio
use_camera
read_bookmarks
wifi_info
switch_mobile_network_state
switch_wifi_state
sim_info
network_info
android_id
access_media
read_external_storage - not implemented in alpha
write_calendar
write_call_log
write_contacts
write_bookmarks
write_external_storage - not implemented in alpha
account_authenticator
read_sms
write_sms
read_mms
write_mms
network_state

Edit:
Alternative Module : Xprivacy (suggested by @beeshyams)