I'm a bit confused here because of "rádi", I'd like to see the conjugation of the present form for "mít rád" but I can find just the followings:
Because rád is an adjective in the short (nominative) form with an adverbial meaning. See it separately https://en.wiktionary.org/wiki/r%C3%A1d#Declension It is the same table as you linked in your first link but with description in English.
If "we" happen to be women, can we not say "Máme rády zvířata". I think that rádi is assuming male animate - is that right? Otherwise I'm very confused about conjugation of mit rád.