Can a star fall in a super massive black hole without getting destroyed? This is the first of many similar questions I have to build up to a specific question or scenario that I want to explore and find an answer to.
Yes, it is easily possible, but it depends critically on how massive the black hole is. A simple calculation will suffice.

If we take a Newtonian approximation for the tidal acceleration across a star of radius $R_*$ as it reaches the event horizon
$$ a_{\rm tidal} \sim 2\frac{GM_{\rm BH}R_*}{r_s^3}\ ,$$
where $r_s = 2GM_{\rm BH}/c^2$ is the Schwarzschild radius.

The gravitational acceleration at the surface of the star, due to its own mass is just
$$a_* = \frac{GM_*}{R_*^2}\ .$$

If we take the ratio of the two, we can assume the star will survive being ripped up before it crosses the event horizon if this ratio is less than $\sim 1$. i.e. when
$$\frac{a_{\rm tidal}}{a_*}= \frac{c^6 R_*^3}{4G^3 M_{\rm BH}^2 M_*} &lt;1$$

The tidal acceleration reduces markedly for high mass black holes. We can rearrange this inequality to give us the minimum black hole mass for survival:
$$ M_{\rm BH} &gt; \left(\frac{c^6 R_*^3}{4G^3 M_*}\right)^{0.5} = 1.5\times 10^{8} \left(\frac{M_*}{M_{\odot}}\right)^{-1/2} \left(\frac{R_*}{R_{\odot}}\right)^{3/2}\ M_{\odot}$$

To first order, this is almost independent of the type of star swallowed. It depends on the inverse square root of the average stellar density, which doesn't vary a lot.

This means that a star could fall into a black hole like that in M87 ($M_{\rm BH}\simeq 6\times 10^9 M_{\odot}$), but  would not survive to the event horizon of Sgr A* ($M_{\rm BH}\simeq 4\times 10^6 M_{\odot}$).

I think in practice this calculation can only be accurate to factors of a few. I have not taken into account shearing forces that would be present for a rotating black hole, or the compression due to tangential tidal forces, or any heating effects from hot gas near the black hole, or interaction with an accretion disk. A full hydrodynamic simulation is needed (and perhaps has been done?).

Also note, this calculation is just for getting past the event horizon. The tidal forces grow as $r^{-3}$, so any normal star will be ripped up shortly after this, even for the most massive black holes we know of.

Please note: This answer is written from the point of view of the falling star. A distant observer will not see the star (or anything else) cross the event horizon.