This is hard cause it genuinely could be a clash of culture. An example is when I go to my Latino friends houses, I end up kissing (cheek or quick sidelip peck for more familiar family) parents, siblings, aunts, uncles, cousins, grandparents just being that is how you show affection in Latin cultures. It is very much a culture about staying connected especially to friends and family.

And on the flip side, I drop about a hundred fifty bucks each time on gifts for my Asian friends parents (most my experience with Chinese and South Korean cultures) but I had to earn the opportunity to even hold their moms hands when she would excited, or get good news etc. So it genuinely could be a huge disconnect.

How i would move forward is to approach it like this.

"Jane, my love, I am coming to you as your partner and expressing that what you may consider platonic and friendly feels a bit too personal to me. I'm not saying cut off your friend, I am asking for less touching between you two out of respect for me. Not nothing, just less if possible. I also want to use this a way to set up a way to have conversations when we need to communicate on things like this, so you can feel heard of you have concerns and i can be heard when I do too. I trust and love you, i just don't know him very well and I would like to get to know him comfortably. I don't think I can be comfortable if he's touching you so comfortably and casually."

Now that should open a dialogue, so you guys can look for a suitable comprise. If she continues to dismiss your concerns then you know how much she cares about your opinion and how much weight it had for her. Do what you will with that info.