Could a character with both the Magic Initiate and Ritual Caster feats understand magical writings enough to use spell scrolls?

The rules for spell scrolls say

if the spell is on your class's list you can use an action to read it... otherwise the scroll is illegible.

So with those feats you have spells from a class's spell list, which means you are technically a spell caster, and whichever list you choose is technically your spell list.

If you have the Ritual Caster feat, you gain an arcane book, which implies that you can interpret and use spells by reading arcane texts (your ritual book) and spell scrolls are arcane texts, so you should be able to use spell scrolls, if wizards can read other wizards spell books there is evidence for a kind of universal magic language that casters use to read scrolls and books, this feat seems to give you access to that language.

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.

This implies that you can interpret spell scrolls, which seems to convey that they are not illegible to you (see below about magical language). And the description of scrolls implies that the only requirements for using a spell scroll are being able to read them and cast spells. These feats should allow you to do both.

Am I right?

The following is not supposed to be a second question. A big part of this question is whether or not there is a magical language. For example once you have a level in wizard you can now read spell books, if you have a level in druid you can read druid spell scrolls. So wizard a ritual caster can read the "wizard spell language" the language wizard scrolls are written in, gaining a level in wizard allows you to read and cast scrolls in that clases Individual "magical Language", as a ritual caster you can have wizard spells and can read wizard scrolls. So you must know the same language which should allow you to cast spells though scrolls. Because you are capable of reading and understanding said scrolls and are capable of casting spells. Casting a spell with a scroll is reading it and casting a spell. With both you should have the knowledge and power to do both.

Magic Initiate: No

Having the Feat 'Magic Initiate' does not grant the character an additional class. Since the rule for spell scrolls is:

...if the spell is on your class's list...

The character would still not have the spell in its class list if it did not before the Feat.

Ritual Caster: No

A ritual caster can only cast spells from their ritual book. The Spell Scroll can be used to add a new spell to the ritual book, but don't forget more of what Ritual Caster says:

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

It seems that the Ritual Caster is a more specific rule than the generic rule about Spell Scrolls, so it follows the player can use the spell scroll to add a new ritual long as you follow all the rules of the Ritual Caster.

There are three questions to answer here.

You are trying to argue around the rules, and complicating your question to do so. But the answers you are looking for are clear from the Player's Handbook. Rules as Written, here the answers. Your DM may rule differently, but the intent of the authors of the game is clear.

1. Does the Magic Initiate feat allow you to cast spells from spell scrolls: No.
   
   This is a duplicate of the question Does learning a spell through the Magic Initiate feat allow me to cast that spell from a spell scroll?




2. Does the Ritual Magic Feat allow you to cast spells from spell scrolls: No.
   
   It does exactly what it says. You may "only cast Rituals from the book." You may copy them to the book.



3. 
   

   Is there a universal magical language? No.
   
   If there was, a wizard could copy any spell of any class list into his book. Any spell caster who can read spells (Wizards, Warlocks with a Book of Ancient Secrets, and anyone with the Ritual Caster feat) could cast a scroll of any class. They can't. Why? because there isn't an actual universal language.

   
   
   

   That is supported also by the entry on wizards spell books. The player handbook makes copying spells into a wizard's spellbook take time, money and risk; and it explains that it is this way because each wizard writes their spells in their own notation, and it takes time to translate the spell from one form to another with care and study:

   
   

Copying a spell into your spellbook involves reproducing the basic form of the spell, then deciphering the unique system of notation used by the wizard who wrote it. You must practice the spell until you understand the sounds and gestures required, then transcribe it into your spellbook using your own notation.

From that we get

If you don't get the ability to cast scrolls from either Magic Initiate or from Ritual Magic, there is no source from which you get the ability by having both.