IIN that my mom has a girlfriend younger than me

We shouldn't judge people because of age differences.

I for one am glad of this counterexample to the common stereotype of an older man and a younger woman (although there are plenty of real-life examples to support the stereotype. Just today an acquaintance told me she was engaged--to her best friend's father, which she finds really amusing. There's over a 30 year age difference, but she's far happier than in her previous relationships). Certainly there are plenty of other examples as well. Groups of people looking for any age combination you can think of. Or at a real life event for young people years ago, there were two organizers, boyfriend and girlfriend. Clearly she was several decades his senior, but they were happy. There's also an entertaining podcast/audiobook I listened to recently, "Owning Regina" by Lorelei Elstrom, of two women in a yoga class, with a significant age difference, both of whom thought they were straight, becoming highly attracted to each other and falling into an energetic BDSM relationship. Supposedly based on a true story.

Ah, but listen to me ramble! The point is that many people pursue romantic relationships with large age differences. The next question is if there is something wrong with that.

As long as the people are of legal age and have the maturity and soundness of mind to make relationship decisions for themselves, I don't see the harm. Almost all concerns you might have about such a relationship would be the same as in an equal-age relationship. The one exception would be that in a long term relationship, the older partner is likely to suffer ill health and even death sooner than the younger. This is a very serious concern that all parties in an age-gapped relationship should consider, but they have the right to consider the risks and make their own decisions.

I assume that you don't have any specific concerns about their relationship--that one of them is likely to cheat on the other, or is trying to get the other's money or some such? If not, then what's the harm of the age difference?

Then we get to their public displays of affection. Your mother, like every other human being, has the right to be a sensual, sexual creature, to have her own desires and pursue them in her own way. But it's understandable that you may feel awkward being around them as they make out.

What would you do if you had a roommate who constantly had her boyfriend over and was making out with him and you weren't comfortable? Your choices are the same:
1. Deal with it. Learn to accept it as part of life and don't let it bother you. But it's certainly understandable if you can't.
2. Set boundaries. See if they can make an effort to restrain themselves to when and where you aren't present, or likely to wander in. Of course, given that it's your mom's house and not yours, that might be a tough sell.
3. Move out. Get your own apartment or find roommates to stay with. Your living expenses will be higher, but you'll have more independence, and possibly more privacy.

Hope this helps! The situation may seem odd to you, but don't worry. Your mother is not crazy. She just has unusual tastes.