Why are you unnecessarily complicating things up? :D
Its well known that by worshiping Gods we can get both Bhukti (worldly pleasures) and Mukti (liberation).
For example, here is how Lord Shiva describes the greatness of Sri Vidya sadhana in JyAnarnava Tantram:
Vaktra Kotisahasraisthu Jihvakotisatairapi| Varnitum Naiva Shakyem
SriVidya Shodashakshari || Vaikhari VAchyabhAvatvAdasagunavarnane | Yato> Niraksharam Vasatu PArA Tatraiva KAranam || MukibhutA Hi Pasyanthi Madyama Madhyama Bhaveth| BrahmavidyAswarupA Hi BhuktimuktiphalapradA|| Ekoccharena Deveshi VAjapeyasya Kotayah| AswamedhasahsrAni PrAdakshinam BhuvastathA|| KAshyAditirthayatrAh Syuh SArdhakotitrayanmitAHA|| Tulyam Na YAnthi Devesi NAtra KAryA Vicharana| Ekoccharena Kim Purnabrahma Kevalam|| ShodasArna MahAvidyA Na PrakAshyA KadAchana | GopaniyA TwayA Bhadre Swayoniriva PArvati||
[Lord Shiva says to Devi Parvati] The greatness of the Shodashi
mahavidya can not be described even if one has thousand crores of
mouths and hundred cores of tongues. If the mantra is uttered only
once one gets the results of performing crores of vAjapeya yajnas and
thousands of aswamedha yajnas. This vidya is brahmavidya and is the
giver of both worldly pleasures and liberation..... Never ever
disclose this vidya , it should always be kept secret like your yoni..
Even Yogini Tantram says the same about the same vidya or sadhana:
BhuktimuktipradA VidyA Anthe Kaivalya DAyini ..
This vidya is the giver of both spiritual and material benefits and in
the end is a giver of kaivalya or moksha.
Also, As You reap what you sow, there is no possibility that the God
will help you to accomplish material things in your life
There is no contradictions here. If you worship God then you are making him happy and if he is happy everyone is happy. So, if you are worshiping God even for your own benefits you are indirectly adding to every being's happiness by doing so. So, this act is an act which results in universal welfare.
For example, see what Lord Sadashiva says to Sri Adya in Mahanirvana Tantram's 4th chapter:
Twam Sarvaswarupini Devi SarveshAm Janani ParA| TushtayAm Tvayi
Deveshi Sarvesham Toshanam Bhaveth || (verse 24).
.......... When you are happy everyone is happy.
So, even if you are worshiping God with selfish motives you are indirectly adding to the well being of every creatures in this universe and you are also helping in the proper functioning of the universe. So, you are bound to get both material and spiritual benefits out of it.
Does worshipping/believing God for sake of liberation is optional
though recommended only? Not mandatory?
Liberation is achieved only when we realise the self. This has been mentioned in the Vedas as well as in the Agamas. And, there is no other way.
Now, there are paths ( like Yoga for example) where worshiping Gods is not required in its usual way but still some sort of internal worship and involvement of mantras are there. And Yoga is one of the valid paths to liberation.
So, IMO the answer is- no its not compulsory. (NOTe : I will support this point with scriptural quotes later, for the time being consider this answer as a partial one.)