Educate yourself on the allergies/sensitivities of your guests. Ask your guests to provide them in writing. This will lessen the margin of error.
If you are having the event catered, make sure the provider is well informed of the allergens and review the menu with the guest with the allergens. Ask for their input.
Think and cook simply. The fewer the ingredients, the higher chance for success.
Be conscious of cross contamination. When prepping ingredients, sanitize knives and cutting boards with an oil disintegrating dish detergent between each ingredient to prevent cross contamination or use separate utensils and cutting boards for different items. Using paper plates as cutting boards can reduce the chance of cross contamination.
When hosting those with airborne allergens, be aware if you have cooked something with that airborne allergen. Allow plenty of time to air out your home and use air purifying machines to eliminate the allergen well before your guests arrive.
Try “make your own” dishes where you provide a main ingredient and allow your guests to create their own meal. For example: A baked potato bar, pasta bar, salad bar or taco/fajita bar. Make sure to keep the “add your own” ingredients separated. With high allergen ingredients like nuts, onions, dairy; make sure to keep them in airtight containers carefully labeled. If you are prepping the ingredients, make sure to monitor for cross contamination.

Have a potluck and ask people to bring a favorite food that is safe for them and enough to share. Require all guests to label all ingredients in their dish. Encourage them to print out a recipe if they would like to share.
Theme parties can be a fun way to have a gathering with food allergy guests. For example, serve just one type of food like an appetizer, tapas, just desserts, soups, fondue, or pasta.
Have a “walk in my shoes” party. Give all the guests a list of allergen safe ingredients and see who can come up with the best tasting creative dish using only those ingredients. Have guests vote on their favorite and award a prize to the winner.
Make specialized plates for those with allergies to separate them from your other guests. Use your fancy or special occasion dishes to ensure there is no chance for miscommunication and to make your guest feel special.