Why is there no stars made of bosons? Consider the white dwarf (or similarly neutron stars), which can be modeled as a star made of degenerate Fermi gas:

A white dwarf, also called a degenerate dwarf, is a stellar core remnant composed mostly of electron-degenerate matter.

So that the star does not collapse because of degenerate pressure.
Question
Is there a bosonic star analog? But in that case, there is no degenerate pressure for bosons because they condense. What keeps the boson star from collapsing?
 A: It's hypothesised a boson star could exist. These bosons would need to repel each other. For example, they could be alpha particles, or axions.
Unfortunately, the boson density needed to form such stars was only available primordially. However, those of too little mass to eventually become black holes may have persisted to the present day. They have been considered as an alternative to supermassive black holes in galactic cores.
A: Just as an aside. It is possible that boson gases do form in the interiors of neutron stars at high densities (e.g. Maruyama et al. 2018). The candidate bosons that form are pions or kaons. I suppose you could call these partial boson-stars.
The formation of a bosonic gas certainly could lead to instability. There is no degeneracy pressure, but a bosonic gas has ideal gas pressure just in the same way that all "point-like, non-interacting" particles would.
However, if you increase the density too much then, contrary to the fermionic case, it is possible for the bosons to form a condensate with a large fraction of the particles having zero momentum and not contributing to any pressure at all. This is unlikely to be a stable situation...
