I wouldn't. Of course, in my country cryptocurrency profits are for free because the high court of the EU declared cryptos as a currency (if you go on holidays outside of the eurozone, you don't pay taxes either for the foreign fiat currency you buy right?)
If the situation is different in your country, I'd argue that they aren't realized profits yet until you convert to fiat? You could still lose it all (from their perspective) so would be useless to pay taxes on income you never realized right?
But I'm not a lawyer.
In the US this is kind of a grey area. The question is whether exchanging one crypto for another is a "like kind" transaction. If you sell one pasture and buy another that is considered a like kind transaction and you don't have to pay taxes, you just carry the basis forward. But if you sell one stock and buy another that is specifically not considered like kind and you have to pay taxes.
The IRS hasn't ruled on crypto as like kind or not, but most people who have looked into it, including myself, think it's not. So if you sell appreciated Bitcoin to buy Monero you have to pay taxes on your gain in Bitcoin. Even if you decide to claim like kind on crypto transactions you have to report the transaction to the IRS, so they will know who to come after when they finally make a ruling.
The one thing you do not want to do is fail to declare your crypto transactions to the IRS. They WILL find you.