Traditionally, the -rid element is significant in names in various languages derived from Norse. It's typically pronounced more like "ree" or "rih" than like the English word "rid", as in to get rid of something:
Astrid > Ástríðr > áss "god" + fríðr "beautiful, beloved, fair".
Sigrid > Sigríðr > sigr "victory" + fríðr "beautiful, beloved, fair".
Ingrid > Ingríðr > Ing (god/ess name) + fríðr "beautiful, beloved, fair".
As you can see, these names have already evolved (or at least, been exported and transliterated). Some people might prefer Astri (or Astrie, Astry, Astree) rather than Astrid in the same way as other simplified English spellings - Zoey for Zoe, Jorja for Georgia, Bree for Brígh, etc. Some phonetic spellings have become traditional and well-established over time - Elspeth for Elizabeth in Scotland, Debra for Deborah or Barbra for Barbara in the USA, etc.
So, completely up to you as the baby's parent(s). Personally I would use Astrid, as it's a contemporary name in use and well recognised internationally. With both Astrid and Astri, if you're in an Anglophone country, you're going to be correcting people who pronounce the first syllable as "ass" or "ars" rather than "ahs/ohs", so it's not much more trouble to correct the whole name.