Are there any REAL advantages to affiliating yourself with a certain political party (other than getting to vote in some primaries?)?

no advantage unless you plan on running for office

It depends on what you consider REAL advantages. I can't tell whether YA ate your Details, or you just didn't provide any.

If you are going to be involved in electoral politics, it's generally in or for some party. There's no downside to registering in a party.

It's all what you make of it really. It isn't much different than how any organization is set up, just a different name and cause. If it's all a good crew that does good, it will be successful, but that 'one in every crowd' can and will try ruling it, taking the most from it, and spoil the whole thing for all, including themselves

That's the entire purpose of "registering" with a party. ALL you are doing is telling your State you want to vote in that Party's primary. You ARE NOT a MEMBER of that party by doing so.