How should I act when my girlfriend meets my homophobic family?

I (19F) am turning 20 in a couple days. My family is going down to Florida on a family vacation during this time frame. My long distance girlfriend (19F) goes to school down there, very close to where we’ll be visiting. It all ended up being very convenient that I’d be by her on my birthday, which I am extremely excited about.

We tend to see each other every couple months, but I always visit her, never the other way around. I’ve met her family, but she hasn’t met mine. This is very deliberate, as a good portion of my family is homophobic. My mom is extremely Christian, and basically refused to talk to me when she found out I was dating a girl. My dad doesn’t think it’s right, but wants to know about my relationships and meet the people I care about. My sister is less likely to say something out loud, but is also homophobic and might make snarky comments/give dirty looks. My brother is the only person in my immediate family who isn’t homophobic. He’s straight, but has a lot of queer friends, and even got to hear about my girlfriend from me before I started dating her. I’ve dealt with all of this since I realized I was gay in middle school. I am used to my family and how they treat me, but I am not used to it being directed at someone I love. My girlfriend’s family is not homophobic, and she is not used to dealing with a family that is.

All that context aside, I asked my mom if my girlfriend could come to my birthday dinner. I don’t know if it’s a smart idea, but I’ll be so close, and I want to spend my birthday with her. My mom conceded, but asked that we don’t kiss or hug or hold hands. I don’t know what to do. It’s very against who I am as a person to change myself to make other people more comfortable. I barely ever get to see her, and it’ll be on my birthday. It makes me so sad that I’d have to ask her not to touch me the entire day. She’s never had to do that to please her family before. I don’t want us to have to be smaller to make my family happy, but I also don’t want them to make issues. I’d fight for her, if an argument broke out, but I don’t want her to have to experience that. I don’t want my birthday to be clouded over by my family being disgusted by me.

My dad told me it’s impossible to avoid. He wants to meet my girlfriend, but told me we should play it safe to make everyone happy. Should I give ground to them, and act as platonic as possible? Or is there maybe something I can say/do to make the day go smoother?

Thank you.