Do we really have to invite 2nd cousins?

If you only speak to them once a year, don't invite them. You want your closest family and friends at your wedding - not people who you could almost pass off as strangers or acquaintances.

I'm not inviting some of my first cousins because we don't speak to each other. I definitely wouldn't invite second cousins that I rarely see.

Whatever you do, don't invite some second cousins and not invite all of them. That causes drama. It's either invite all or don't invite any.

This seems fine to put a cut off here, especially if you are not close to them, and especially if you are not inviting all of them. It's not like some are being invited and others are not, you're just making a blanket decision that will apply to all of them. Seems like a practical choice.

I wouldn't invite anyone that you don't speak with on a regular basis.