I am considering reclassing from Infantry to MP. What’s the process to go from National Guard to active duty Army for MP?

The first step would be to see a recruiter to see if he can get you a MP slot. Then he should give you a DD Form 368 Request for Condition Release. This needs to go up your Chain of Command to be signed by the first General in your chain or his designated representative. That process can be slow, but it never hurts to ask the Chain of Command if you can hand carry it to the appropriate authority. Once you have that, you basically enlist in the Army.

My advise and this is coming from a former MP, is not to become an MP. The two worlds civilian police and MP don't mix well. Not to mention I did more security guard duties than actual law enforcement.

It's either going to be MP transition course or you'll be an insert with the AIT phase of OSUT. The transition course would more likely be the case if you were thinking of staying guard side BUT a lot of our schools are now with our active and reserve counterparts. BLC for example is 5 weeks for the guard when it used to be two. A buddy of mine just went thru 31E school and he was an insert and gone for 8 weeks where as I was only gone 2 in 2012.
And no, your civilian leo experience doesn't keep you from going to CID school. There is a program available to civilian law enforcement who qualify with certain credentials to work for the Army as CID or enlist as a 31D as it's a school for E5 and above, but you still have to be MOS'Qed.