As someone who worked in a tack shop for several years, we always suggest the brand leather cleaner and conditioner. If not, we advise to stick with a product designed for that type of leather/region.
From my training and experience a German leather cleaner such as lederbalsam can strip the dye from nice English, Italian or French leather. German leather has a different tanning process that allows it to take a ‘stronger’ cleaner/conditioner. Similarly, English leather has a better result with a product designed for it.
Examples:
Albion, MadCow or Rapide Leathergel products on Albion/Baines/Fairfax/KL Select leather
Lederbalsam on Stubben/Passier/Dobert leather
Belvoir/Devoucoux on Butet/Devoucoux/Voltaire
Amerigo cleaner/conditioner on Amerigo or Italian leather
I still remember calling a client that cleaned their saddle with a German soap (I hate that I keep saying Lederbalsam but that’s all that comes to mind at the moment) to tell them that it voided any claims against leather quality/issues.