One of the most common interactions you will deal with comes from cards such as but not limited to Effect Veiler, Infinite Impermanence, Fiendish Chain, and Forbidden Chalice. There are two situations you need to be aware of when playing this deck. The first one might seem obvious, but if your opponent targets one of your fusion monsters with a card like Effect Veiler - There is nothing that stops you from just chaining your fusions monsters effect to tag out. That being said, if you allow for your opponents effect to fully resolve you will no longer be able to RESOLVE your fusions effect when attempting to tag out. Meaning: if you return your fusion to extra deck as cost, you will lose your fusion and will NOT summon your banished Ritual Beast monsters.
The second interaction within this subset of cards revolves around them being used in response to the summon of Ritual Beast Tamer Elder. This also works in your favor due to the way that Ritual Beast Tamer Elder is worded. The way that Ritual Beast Tamer Elder grants you an additional summon is not in the form of an effect that activates on summon, but instead by placing a condition onto the duel once successfully summoned. This means that the only way to "negate" his effect would be to either negate the summon entirely or to have a card such a Skill Drain already face up on the field prior to the summon of Ritual Beast Tamer Elder.

While already being an extremely good hand trap versus any combo based strategy, Nibiru, The Primal Being also has a quirky interaction when played in Ritual Beast. The set up for this play is fairly simple, it requires you to have a Nibiru, The Primal Being in hand while also controlling a Ritual Beast fusion with the ability to tag out. Any time after your opponents 5th summon you can activate your fusion monster effect to tag out by returning it's self to extra deck as cost, you can then chain your Nibiru, The Primal Being from hand.

When resolving, Nibiru, The Primal Being will first tribute all face up monsters on the field to summon it's self and a token. After that resolves your fusions effect will resolve summoning the two banished Ritual Beast monster your targeted.

Much like the play with Nibiru, The Primal Being this interaction is based on our fusion monsters being able to return to the Extra Deck as cost. The requirements for this play are that you control no other cards besides a Ritual Beast fusion monster with the ability to tag out.
During either player's turn you can activate the effect of your fusion monster; returning it to the Extra Deck for cost, then you can chain Infinite Impermanence from your hand.

This is just some common interactions, in using Ritual Beast Steeds in response to cards like Skill Drain, Effect Veiler, Infinite Impermanence et cetera.

It is pretty simple, in concept, but people tend to overlook some of the most simple things -- in this case, when you activate any of your effects, and your opponent responds with any card similar to those listed above; you simply use your Ritual Beast Steeds, and upon resolution you destroy your own monster, to ensure the effect goes through, as it will no longer be face-up on the field to be negated.

Ritual Beast Steeds allows you to destroy monsters on the field up to the number of Ritual Beast monsters you control. Nothing in its text states you can not use its effect to destroy your own monsters.
This is a great way to clear your field during the End Phase to get rid of Mystic Mine. This is also helpful when dealing with Evenly Matched as it allows you to destroy your monster before they would be banished face down.

Returning to the Extra Deck is not apart of the effect that happens on resolution. Instead it is the action that must be preformed to activate the effect. This means that even under Skill Drain you will be able to pay cost and return that monster to the Extra Deck. This only maters due to the way Skill Drain is worded, Skill Drain only negates the effects of monster while they are face-up on the field. Meaning once your monster has returned to the Extra Deck it is no longer negated by Skill Drain and will resolve as intended.

Moreover, if you were to use Ulti-Cannahawk effect to search and then chain its other effect to "tag out"- It would be in the Extra Deck when resolving thus no longer be negated by Skill Drain.

If the normal summon of Spiritual Beast Tamer Winda is negated by Solemn Judgment you will still be granted the effect of Spiritual Beast Tamer Winda. In Yu-Gi-Oh the term "possession" unlike "control" is not limited to cards on your side of the field. This means even though the summon was negated, Spiritual Beast Tamer Winda was still in your possession when destroyed.