I have never been turned down to dive with any shop or resort because of the shape, color, or origin of my card. Now with that being said, I don't carry a card with me, my wallet is not big enough. There are stores though that will deny you of certain things, and the easiest solution is find another store. Most on here will agree, in the retail side of the Scuba Industry, money talks, and the stores will take your money no matter who's card you show. On the resort side of things, most shops see so many cards a day, they could care less what card you show as long as it says you are certified and it has a way to identify you (a picture of you). You may run into a young shop employee who is just getting into the industry that has no clue any other agency exist, except for the one he was certified through. Take his rant with a grain of salt and ask to speak with a supervisor. Ginnie Springs is starting to become a staple in the Northern Florida area for this. They hire some young teenagers to run the store front, and most have no clue that there is more to diving other than PADI or SSI. Simply ask for a supervisor and problem solved. As most others have stated, seek as much training as you can, it will only make you a better, safer, more proficient, and a more confident diver. Happy Diving.
Here is a list of my certifications to date, so in my opinion, agency jumping is just fine. I would add that if you go pro, stay with one agency till you hit the Instructor level then jump agencies. Some agencies will not accept a Dive Master or Assistant Instructor rating from other agencies, but the majority will take direct crossovers from full Instructor status. Once you have reached the Instructor level, then start jumping agencies again. This saves money, because you don't have to take multiple Dive Master and Assistant Instructor courses.
CMAS - 3* Moniteur Course Director
SSI - Dive Control Specialist Instructor
Platinum 1000 Instructor
Public Safety Diver Instructor
Full Face Mask Instructor
Deep Instructor
Perfect Buoyancy Instructor
Search & Recovery Instructor
Snorkel Instructor
Ice Diving Instructor
Dry Suit Instructor
Nitrox Instructor
Navigation Instructor
Night Instructor
Sidemount Instructor
React Right Instructor
SEI - Instructor Trainer
Ice Diving Instructor
Public Safety Instructor
Under Water Criminal Investigator Instructor
Full Face Mask Instructor
Dry Suit Instructor
Sidemount Instructor
PDIC - Instructor Trainer
Ice Diving Instructor
Public Safety Instructor
Under Water Criminal Investigator Instructor
Full Face Mask Instructor
Dry Suit Instructor
Sidemount Instructor
Nitrox Instructor
EFR - Instructor
NCOEMS - Level 1 Instructor
PADI - Master Scuba Diver Trainer
Public Safety Diver Instructor
PSD Surface Support Instructor
Dry Suit Instructor
Full Face Mask Instructor
Search and Recovery Instructor
Night Diving Instructor
Deep Instructor
Nitrox Instructor
Emergency O2 Instructor
Under Water Navigator Instructor
Tec Gas Blender
NON PRO LEVEL PADI - Master Scuba Diver
Boat Diver
Nitrox
Drift
Night
Dry Suit
Equipment Specialist
Rescue
Advanced
Open Water