YuGiOh question: Can the effect of a Ritual Beast card affect a Spiritual Beast?

The capitalisation doesn't matter.
Keep in mind that everything is translated from Japanese text, and Japanese kana does not use capitals. Ritual Beast Tamer Elder looks for monsters with '霊獣' in the name, so therefore works with other 'Ritual Beasts' who use 霊獣 and 'Spiritual Beasts' which use '精霊獣'.
The cards have the same effect in English as they did originally, so yes, a Spiritual Beast is also a Ritual Beast, the capitalisation is just the decoration added to written english card names, and does not affect how the cards work.

Other examples - Ignoble Knights work with anything that look for Noble Knight. Note also that all card titles are written in block capitals anyway, the letters at the start of the words are simply bigger. So technically you could say that even Ritual Beast Elder Tamer is not a 'Ritual Beast' written exactly like that, he is a 'RITUAL BEAST', though like I say, the capitalisation does not matter.

Spiritual Beast is a sub-archetype of "Ritual Beast"