Old thread but raises the question of what to lubricate brake caliper rubber seals and pistons with. Some people just use brake fluid. The problem with conventional mineral oil based grease is it can swell and damage the rubber seals. What is used instead is a synthetic grease made from vegetable oil (e.g. castor oil) and goes under the generic name of Red Rubber Grease or RRG. One well known brand is Castrol Red Rubber Grease (Castrol RRG) which is compatible with DOT 3, DOT 4, Super DOT 4, DOT 4 Plus and 5.1 type brake hydraulic fluids. I used this some 30 years ago and have also used just DOT 4 and do not recall any issues. Would be nice to hear of anyone else's experiences.
Note: I have seen silicone grease advertised for this purpose but I have had no experience with this so best to just use a grease that is specifically recommended for caliper pistons and seals and is brake fluid compatible.