When I'm trying to add another spell to either Book of Ancient Secrets or Ritual Caster after the initial 2. When I pick a third spell It clears the drop down box and places the option I've picked underneath it. This happens with all of my characters. I've linked my most recent character below

 https://www.dndbeyond.com/profile/Charleymonk2000/characters/33654554

It shouldn’t be “clearing the dropdown,” it should be adding a new dropdown ready for you to make your next selection.

It's clearing the 3rd dropdown box placing the spell i picked where the 4th dropdown should be and not letting me pick higher than 3rd level spells

Quote from Charleymonk2000 >>

It's clearing the 3rd dropdown box placing the spell i picked where the 4th dropdown should be

 That is the normal way it works, yes.

Quote from Charleymonk2000 >>

and not letting me pick higher than 3rd level spells

 I’m assuming that your character 5th or 6th level?

Ritual Caster

You have learned a number of spells that you can cast as rituals. These spells are written in a ritual book, which you must have in hand while casting one of them.

• When you choose this feat, you acquire a ritual book holding two 1st-level spells of your choice. Choose one of the following classes: bard, cleric, druid, sorcerer, warlock, or wizard. You must choose your spells from that class's spell list, and the spells you choose must have the ritual tag. The class you choose also determines your spellcasting ability for these spells: Charisma for bard, sorcerer, or warlock; Wisdom for cleric or druid; or Intelligence for wizard.
• If you come across a spell in written form, such as a magical spell scroll or a wizard's spellbook, you might be able to add it to your ritual book. The spell must be on the spell list for the class you chose, the spell's level can be no higher than half your level (rounded up), and it must have the ritual tag. The process of copying the spell into your ritual book takes 2 hours per level of the spell, and costs 50 gp per level. The cost represents material components you expend as you experiment with the spell to master it, as well as the fine inks you need to record it.

Book of Ancient Secrets

Prerequisite: Pact of the Tome feature

You can now inscribe magical rituals in your Book of Shadows. Choose two 1st-level spells that have the ritual tag from any class’s spell list (the two needn’t be from the same list). The spells appear in the book and don’t count against the number of spells you know. With your Book of Shadows in hand, you can cast the chosen spells as rituals. You can’t cast the spells except as rituals, unless you’ve learned them by some other means. You can also cast a warlock spell you know as a ritual if it has the ritual tag.

On your adventures, you can add other ritual spells to your Book of Shadows. When you find such a spell, you can add it to the book if the spell’s level is equal to or less than half your warlock level (rounded up) and if you can spare the time to transcribe the spell. For each level of the spell, the transcription process takes 2 hours and costs 50 gp for the rare inks needed to inscribe it.

They're 5th level. To my knowledge the normal way it works is, that when you pick a spell the dropdown box moves down by one and the spell is chosen is placed where the dropdown was

Quote from Charleymonk2000 >>

They're 5th level. To my knowledge the normal way it works is, that when you pick a spell the dropdown box moves down by one and the spell is chosen is placed where the dropdown was

 Do the spells show up on your character sheet?

Yes, They do.

Then it’s working. And I have solved the question as to the spell levels. Everything seems to be working just fine.

I guess it's just that I was discombobulated by an update to the way spells chosen were displayed in the dropdown then.

Happy to help.