Question: Is it alright for Buddhists to just pray as form of respect to deities (gods), but not to request anything from them?
Answer: It is alright for Buddhists to express respect but there should not be a sense of utmost reverence and absolute refuge, as that is reserved for enlightened beings, such as Buddhas, (Bodhisattvas and Arhats), who should first come to mind in times of spiritual need. If there is no difference in sense of devotion or affinity, it means one has yet to understand the supreme nature of the enlightened, which also means the sense of refuge is not genuine and strong enough.
While the Buddha is historical, some worshipped gods might not be real; but only mythological. Still, we can have a general sense of respect for any virtues they represent (even if the depicted character might be flawed in other aspects). Where worship of gods come in, that requires practices against the Buddha’s teachings, such as the ‘need’ for making animal sacrifices (or meat offerings), these should not be participated in.
Related Articles:
Differences Of Refuge & Respect
https://thedailyenlightenment.com/2011/10/differences-of-refuge-and-respect
Difference Between Faith & Respect
https://thedailyenlightenment.com/2012/09/difference-between-faith-respect
I realize from experience that my sincere prayers would be answered regardless of who I pray to.
Not true at all. Non-existent gods cannot answer anyone’s prayer. Not even that of a child or the Pope, as you can see at https://thedailyenlightenment.com/2016/04/is-there-a-god-who-allows-suffering/
Why? Because again, the god prayed to simply does not exist. Not according to all fully enlightened Buddhas and proven reality.