"Vbatt"
You mean... properly filtered, transient protected, and voltage limited, Vbatt, right???
Cars are not gentle environments; be very careful with what you power from automotive supplies!
As for CMOS, it's generally okay to source/sink a few mA into/out of a pin (i.e., current coming from a voltage above VDD or current sinking to a voltage below VSS). The outputs are slightly more robust as they have bigger transistors (one or the other of which is usually active at all times), whereas the inputs just have lossy diodes. I would rate 74HC, LVC and such as having higher capacity than CD4000 or 74C chips, but I still wouldn't suggest going over 10mA DC / 20mA peak with those. Size the pull-ups/downs accordingly, or run them from respective supplies.
Note that, if you use a 7805 to make the 5V rail from Vbatt, you're only moving the problem from the resistors to the 7805. If heat is a problem, use a switching regulator. And speaking of heat -- if operating temperature is also a problem, mind that bog standard 7805s turn off at a paltry 100-120C -- with fairly weak RthJC and even weaker Rth of the heatsink, you can easily blow this spec from just a few watts on a hot, sunny day, in which case the regulator will turn itself on and off repeatedly, until it eventually pops.
Tim