Mirror and reverse text Inspired by I reverse the source code, ...
Your task, if you wish to accept it, is to reverse text and mirror select characters. Yes, yes, I know. Very surprising.
Input
A string, stdin, an array of characters, or any other source of text. All characters of the input are guaranteed to be in the printable ASCII range (32-126).
Output
The reversed text with some characters mirrored. To do this:

You replace any occurrences of the characters (, ), /, \, &lt;, &gt;, [, ], {, or } in the text with the corresponding &quot;mirrored&quot; character: ), (, \, /, &gt;, &lt;, ],  [, }, or {.
and then reverse the text.

You may assume a maximum line length of 255.
Rules

Standard loopholes apply.
This is code-golf, which means that the shortest answer in each programming languages wins. Consequently, I will not be accepting an answer.

Testcases
(s)t/r\i&lt;n&gt;g[i]e{s} -&gt; {s}e[i]g&lt;n&gt;i/r\t(s)
stringies -&gt; seignirts
()/\&lt;&gt;[]{} -&gt; {}[]&lt;&gt;/\()
{s}e[i]g&lt;n&gt;i/r\t(s) -&gt; (s)t/r\i&lt;n&gt;g[i]e{s}
seignirts -&gt; stringies
{}[]&lt;&gt;/\() -&gt; ()/\&lt;&gt;[]{}
qwertyuiop database -&gt; esabatad poiuytrewq

As seen above, the output should go back to the input if run through the program again.
Sandbox link
Python 3, 61 60 59 bytes



lambda s,t="(/&lt;[{}]&gt;\)":[(c+t)[~t.find(c)]for c in s][::-1]


Try it online!

 -1 byte thanks to @xnor. 

Changed the lookup string, so that the c in t test is eliminated.



Python 2, 63 bytes



lambda s,b='(/&lt;[{}]&gt;\)':map(dict(zip(b,b[::-1])).get,s,s)[::-1]


Try it online!

-1 byte thanks to @xnor.

Python 3, 65 64 bytes



lambda s,b=b'(/&lt;[{}]&gt;\)':s.translate(dict(zip(b,b[::-1])))[::-1]


Try it online!

Just for fun using idiomatic Python. (More idiomatic would be using str.maketrans, but it's way too long.)

-1 byte for both because the \ in '\)' doesn't need to be escaped.