In my single player world, I cannot place a saddle stand or horse armor stand. I have the 1.12.2 version most up to date

Closing due to inactivity

Have you tried simply right clicking when holding them just like any block?

Yes I have, I'm wondering if it might be a conflict with Harvest craft

In these older version, harvestcraft is only known to affect foodstuffs items, not the stands

ok yep. That was not the issue. Are there any other conflicting mods that are known of?

There are no known issues that would cause the stands to not be placeable. Keep in mind that the stands are just like regular blocks, and not placeable items. When placing them there is no need to hold shift while placing them.