From my understanding with cryptos like bitcoin, address reuse is discouraged because it makes the funds on the address more vulnerable to being compromised. Is Tezos the same way or is it okay to perpetually reuse the same address. If so, why/how is Tezos different?
I'm not a cryptographic expert but, the issues that you mentioned in Bitcoin involved weak signatures (same K value bug), which when used multiple times enabled the guessing of the private key. This has now been fixed.
There is still a case for advocating against address re-use, especially for addresses used for long term storage of large amounts of value: quantum computing. It's still early days, and there's no indication of any imminent threat to current cryptographic schemes. However a Tezos address that remains unrevealed (i.e. full public key not made public) should in theory be harder to crack than one that has been revealed.
The biggest reasoning why not to re-use an address is for 'connecting the dots' and identifying who an address belongs to. If you're ok with that, reuse the same address as long as you like.
In Tezos, 2 key actions are locked to an address, so switching is difficult. A baker will always use the same key because their baking rights, and rewards, are tied to the address the register. If a bakery needs to switch address, they must convince all of their delegators to switch as well. No guarantee they will switch.
On the same line, when you delegate to a baker, the delegation is tied to that address and your rewards are, generally, sent to that same address. It is much easier to switch addresses as a delegator; you can simply empty the contents from address A to address B and then delegate B.
This is very comparable to bitcoin as when you join a mining pool, you specify a single address to receive rewards.