I'm trying to create characters for a family one-shot and I'm trying to give them as many character options as possible. I have the Player's Handbook 2024 Edition, Monsters of the Multiverse, and Humblewood. I'm trying to make the races/species (and backgrounds) in the latter two be compatible with the 2024 Handbook. What would be an easy way to do this? 

You shouldn't need to do anything to the Species options, really. The only thing that might come up (probably not for Monsters of the Multiverse, but maybe for Humblewood, I'm not sure) is that if they have species-granted spellcasting, the player should be able to choose the spellcasting ability, rather than it being set per species like it was for e.g. 2014 Tieflings.

As for backgrounds, 2024-style backgrounds have the following elements:

• Two skill proficiencies
• One tool proficiency
• One Origin Feat
• Three ability scores (which the player can either gain +1 to all of, or +2 to one and +1 to another one)
• A starting gear package worth 50 gp

Older backgrounds that don't have those things (especially the feat) need to be reworked so they do.

Thanks a lot! Should I remove the ability score increase for the species? I also think that the older species have more traits than the newer one.

Yes, under 2024 rules, ability score increases are supplied only by the background, not the species.