Is it permissible for Muslims to celebrate innovated feasts such as marriage anniversaries, birthdays or any others?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

Allaah The Almighty has granted Muslims two feasts ('Eeds): Al-Adh'haa and Al-Fitr. Anas narrated that when the Prophet, sallaallaahu ‘alayhi wa sallam , went to Madeenah and found its people celebrating two different days that they used to celebrate before Islam, he told them that Allaah The Almighty had replaced those two days with Al-Adh'haa and Al-Fitr. [Abu-Daawood]

Had there been feasts for Muslims other than these two, the Prophet, sallaallaahu ‘alayhi wa sallam, would have told his Companions and his Ummah (nation) about them. Thus, any other feast is considered an innovation. The Prophet, sallaallaahu ‘alayhi wa sallam, warned us that anyone who makes an innovation in religion, it would not be accepted from him. [Muslim]

There is nothing wrong with feeling joyful on the occasions mentioned in the question, as this is a natural reaction that people are born with. However, it is prohibited to make a feast because of them and then celebrating them as a habit year after year. It should be known that states and individuals’ keenness on making celebrations for various occasions results only from their ignorance of the rulings of the Sharee’ah and the limits of what is lawful and prohibited. It is also an outcome of imitating other nations who follow their personal desires and invent a feast for every single occasion. Sadly, some ignorant Muslims admire and imitate them. Hence, these innovated feasts involve many violations of Sharee’ah, such as imitation of disbelievers and introducing innovations in religion.

Allaah Knows best.