Is it normal for a homemade dipole to work before you tune it?

An SWR of 1.5 at the low end of the band is a really normal result for a dipole cut with a formula, expecially if you added a bit extra for the solder joints and rope stretch. You probaly just landed close. The climbing SWR as you go up the band is exactly what a center-fed wire does, since it drifts further from resonance as you move away from the frequency you cut it for. Nothing wierd there. As for the radio folding back power, most modern rigs don't start backing off til the SWR is up around 2 to 1 or higher, and even then the reduction is gradual. If you want to check, key down at full power into the antenna and watch the power meter. If it reads close to your set power, you're getting out fine. If the meter shows less than what you dialed in, that's the foldback happening. At 1.5 you'll almost certainly see full power. wether to trim is honestly up to you. If most of your operating is at the bottom of the band and you're making contacts, there's no urgent reason to touch it. A 1.5 SWR only costs you a fraction of a dB compared to a perfect match, wich is nothing in the real world. If you do decide to prune, just snip equal amounts off both ends, a little at a time, and recheck. Trim long rather than short, because you can always cut more but you can't uncut. Keep the offcuts and some spare wire around in case you ever want to add length back.

Long term, running it as-is won't hurt the radio. The finals are happiest below about 2 to 1, and you're well inside that. I've run antennas at 1.5 or worse for years without a problem. If you ever want to work the higher end of the band more comfortably, that's the point where a little trimming or a simple tuner makes sense, but for now I'd just enjoy it.

Funny, my first wire antenna was speaker wire too. Mine came out long and I had to trim a bunch off before it settled down. If yours is reading that low without any pruning, you either got lucky or your tree is doing half the work for you. Height changes things more than people expect.

One thing I'd add, the insulation on speaker wire makes it act a touch longer electrically than bare wire, so don't sweat it if you're not textbook perfect. Mine's still up there years later. Leave it alone unless something bugs you.

I always used proper crimp connectors instead of just soldering every joint, especially on salvaged wire. It made the entire setup much more secure. When I built my first antenna, I realized the physical stress on the solder joints from the wind was somethig I hadn't considered. Using those connectors meant the wire wouldn't pull out over time, which is a bigger concern than the SWR itself once it's stable. I think the rigidity helps the antenna maintain its intended geometry better, too.

One thing I'd try before touching the wire at all is sweep across the band slowly and find where the SWR actually bottoms out. If the dip sits lower in frequency than where you like to operate, the antenna is running electrically long and trimming a bit off both ends whould slide the dip up toward your segment. If the dip is already above where you operate, leave it alone, because cutting would push it further away. I did this on a wire I strung between two sheds years ago and it saved me from trimming the wrong direction, which I had very nearly done on a hunch before I thought to check. The dip location tells you more than the number at any single frequency does.