You don’t have to be touchy-feely about animals, plants, rocks, etc. to be happy that they are part of God’s Creation, or sad that Creation fell along with its head creatures, Adam and Eve.
It’s true that fallen Creation will not be fully healed until the end of time, the general Resurrection, the new heaven and new earth, etc.
However… it is true that Creation was partially healed by the first coming of Jesus Christ. This was demonstrated in big things (the winds and waves obeying Jesus and His ability to multiply loaves and fishes). Traditionally, Christians also believed that animals obeyed Jesus and were part of the glory of His Nativity, according to His birth in the stable, the prophet Isaiah’s comment (Isaiah 1:3) that “The ox knows his owner, and the donkey his master’s manger,” and the angels announcing Jesus’ coming to the shepherds (and hence the sheep). This was logical since Jesus was the new Adam, and Adam had dominion over the animals. Likewise, the death of Jesus didn’t just make Mary sad; the Sun and Moon covered their faces (as the old saying goes), and the earth trembled. When Jesus was resurrected, not just men but also Creation rejoiced. We can’t tell exactly how this affected the natural world, but obviously it did somehow matter.
Because of this, it was always seen as very fitting for saints to be on good terms with animals, and vice versa. The Egyptian hermit monks made pets of deadly cobras and all kinds of large snakes, and were guarded from danger by these friendly snakes. Monks and hermits (like St. Benedict) were often friendly with ravens and crows (following the example of the prophet Elijah). Many saints had a way with bees. Often hermit saints got along even with wild animals of the most dangerous kinds, because they were so Christ-like and authoritative. St. Francis and the wolf, or St. Anthony preaching to the birds and the fish, are also examples. We won’t even go into examples of dominion over plants, or of inanimate creatures, like water or lava.
This sort of thing is the opposite of worshipping nature or giving animals undue importance. We can appreciate them as both fellow creatures made by God, and as lower creatures than ourselves that need our protection and guidance.