Gautama Buddha and Hindu divinities

He taught that they exist only at the behest of a god feeling at the end of their proverbial "rope".

It's like celebrity the world is their oyster and then the pearl goes missing out of it; at their wits end grasp and cling scamper and scurry.

Standing on the moon?

Stop that noise and just practice so it does not occur again. "Resting on one's laurels" is what the greeks called all: Self or other appointed bouts of fame or recognition.

The grasshopper and the ant; is a good fable for such a thing.

The Buddha and others like him before and after; sat through, stood through, or lay through death until they arose again and were conscious the whole time such thing was occuring... the pain of being eaten alive, the pain of being chopped down like a tree, etc etc. no matter what mode of existence or life one finds themselves in?

Suffering... no matter the form of life suffering exists. Money, fame, and fortune a fools errand to tarry on. Have compassion on them? Hell no... it's the same thing as an enabler it only allows the rise of a system and cycle of abuse to keep occurring.

When Arhats would go see the Buddha; to avoid kamma accumilation from such beings? He would point out that there are: Quick learners, medium learners, and slow learners. Kammic fruition goes both ways... patience was the key to over coming the stubborn Ox; as "A good horse runs under the shadow of the whip." Once his son; knew the whip? "Fetter" was more suiting of a name than horse.

...are we not fortunate to have the entire path to escape that suffering lain out before us? Indeed so, and yet being the path is something else entirely.

Age does not necessarily mean someone is wise or innocent. I have seen the "rainbow bodied" only help to continue cycles of pain and suffering; as it is often a siddhi/riddhi abuse of power used to induce attachment in the weak like a preta preying on peoples weaknesses. Instead of leading to liberation.

The Kalichakra initiative was meant to try to help put an end to the abuse of such a thing... However; it does and it does not it is best seen with direct experience between; Old age and death as "sickness" as the twelve nidana go, not a gate or pathway to liberation.

"Am I right that Gautama Budda did not teach to worship the Hindu Gods?"

Yes, you are correct.

"Did he teach not to worship them?"

For those taking refuge in the Triple Gem (ie., Buddhists) it is advised not to seek salvation in the form of the Hindu Gods. The Buddha taught that salvation or liberation can not be found via worship of the Hindu Gods.

It is important to note that the Buddha was not an active proselytizer disparaging other religions. The Buddha taught the Dharma to those who were interested and had the capacity to understand and take the medicine to achieve liberation. The Buddha acknowledged many times during his life as Gautama, that some sentient beings were not yet ripe enough to understand the Dharma to achieve liberation in their present circumstances. The Buddha even censored himself at times from teaching aspects of the Dharma that practitioners were not ready to understand or hear.

For this reason, today's masters of the Dharma - for instance the Dalai Lama - also do not proselytize and even warn other Dharma practitioners against proselytizing. The Dalai Lama says that Buddhist proselytizing can even lead to more suffering, not less. So it is advised that Buddhists do not proselytize or try and convert unsolicited people.

Actually it appears that the Buddha spoke positively of the use of legitimate wealth for performing oblations or offerings to the gods (who are not immortal or eternal) in the sutta quoted below.

From AN 5.41:

Furthermore, with his legitimate wealth he makes five spirit-offerings:
Puna caparaṃ, gahapati, ariyasāvako uṭṭhānavīriyādhigatehi bhogehi bāhābalaparicitehi sedāvakkhittehi dhammikehi dhammaladdhehi pañcabaliṃ kattā hoti.

to relatives, guests, ancestors, king, and deities.
Ñātibaliṃ, atithibaliṃ, pubbapetabaliṃ, rājabaliṃ, devatābaliṃ—

This is the fourth reason to get rich.
ayaṃ catuttho bhogānaṃ ādiyo.

Lord Buddha did not say not to worship gods. What Lord Buddha did say was not to become unconditional followers/worshipers of gods by neglecting the Triple Gems - The Buddha, The Dhamma and The Sangha.

According to Buddhism, a person who engages in righteous work and prevents from sinful acts might eventually become a god in his/her next life or lives because of his/her achieved merits. Therefore, any god deserves our respect.

For example, no matter our religious beliefs, we bow/respect/worship the King of the country. Because the king is a leader; a powerful person. He is indeed lucky and luxurious. Likewise, we must respect all gods because they are in a far more powerful, meritorious and higher place than any of us combined.

Specifically in Hindu religion, there are many gods with many names. I don't know much about them but that's their belief. It is okay to worship them. As a Buddhist, what's not okay is to abandon the Triple Gems and blindly going on worshiping gods.

For your knowledge, I also added some extra information below too.

According to Buddhism, every single person who still travels though this tough sea of Samsara,

1. Had been
2. Still being
3. Will be

a god for numerous times until he/she attains Nibbana. Anyone who engages in righteous work and prevents from sinful acts might eventually become a god because of his/her achieved merits. But when those merits fades after a long time, then that god will become another living being again. (may be another god, human, animal or a being in hell).

In order to become successful in life, Lord Buddha said "Give respect for those who deserves respect." You can read Singalowada Sutra to get more information about how to show respect and uphold the necessary responsibilities to 6 specific parties. Those 6 specific parties are mentioned as 6 directions and you have to respect/worship/oblige to them. They are,

1. Parents - represented by EAST direction
2. Teachers - represented by SOUTH direction
3. Spouse - represented by WEST direction
4. Friends - represented by NORTH direction
5. Monks - represented by UP direction
6. Servants - represented by DOWN direction

To be a good person is to respect all 6 directions everyday and to make sure that our responsibilities towards them are always met. So that you will get their respect and obligations back.

I hope you got your answer. Wish you well.

Buddhists worship deities that they believe are Buddhas or Dharmapalas. Some deities are closely related to Hinduism or some say the same. But Buddhism is different from Hinduism at its core. It's not only about deities but also about teachings. If a deity confers the Buddhist teaching you might say he/she's Buddhist.